Дисертації: "Quantum spin models"

1

Oriti, Daniele. "Spin foam models of quantum spacetime." Thesis, University of Cambridge, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.620008.

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2

Collins, Alexander Rory Physics Faculty of Science UNSW. "Quantum lattice models." Publisher:University of New South Wales. Physics, 2008. http://handle.unsw.edu.au/1959.4/43408.

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This thesis presents studies of the low energy properties of nseveral frustrated spin-1/2 Heisenberg antiferromagnets using various analytic and computational methods. The models studied include the union jack model, the alternating Heisenberg chain, the Heisenberg bilayer model, and the spin-Peierls model. The union jack model is a Heisenberg antiferromagnetic spin model with frustration, and is analyzed using spin-wave theory. For small values of the frustrating coupling $\alpha$, the system is N{\' e}el ordered, while for large $\alpha$ the frustration is found to induce a canted phase. Spin wave theory with second order corrections finds the critical coupling at $\alpha \simeq 0.645$,which agrees quantitatively with series expansion results. No intermediate spin-liquid phase is found to exist between the two phases. The alternating Heisenberg chain is studied using an alternative triplet-wave expansion formalism for dimerized spin systems, modification of the ??bond operator?? formalism of Sachdev and Bhatt. Projection operators are used to confine the system to the physical subspace, rather than constraint equations. Comparisons are made with the results of dimer series expansions and exact diagonalization. The S=1/2 Heisenberg bilayer spin model at zero temperature is studied in the dimerized phase using analytic triplet-wave expansions and dimer series expansions. The occurrence of two-triplon bound states in the S=0 and S=1 channels, and antibound states in the S=2 channel, is predicted with triplet-wave theory and confirmed by series expansions. All bound states are found to vanish at or before the critical coupling separating the dimerized phase from the N{\' e}el phase. The critical behavior of the total and single-particle static transverse structure factors is also studied by series expansion methods and found to conform with theoretical expectations. The Heisenberg spin-Peierls model with dispersive, gapless phonons is studied with Density Matrix Renormalization Group methods. We investigate the zero temperature properties of the model using the crossover method. The calculations were found to converge poorly and no conclusive results could be found using this method. An analysis of the convergence problems and the discovery of an anomalous triplet ground state is presented in this chapter.

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3

Dowdall, R. J. "Spin foam models for 3D quantum geometry." Thesis, University of Nottingham, 2011. http://eprints.nottingham.ac.uk/11755/.

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Various aspects of three-dimensional spin foam models for quantum gravity are discussed. Spin foam models and graphical calculus are introduced via the Ponzano-Regge model for 3d gravity and some important properties of this model are described. The asymptotic formula for the 6j symbol found by Ponzano and Regge is generalised to include the Ponzano-Regge amplitude for triangulations of handlebodies. Some simple observables are computed in a model for fermions coupled to 3d gravity. The result is a sum over spin foam models with certain vertex amplitudes which are described. An explicit example is given and the vertex amplitudes expressed in terms of 6j symbols. Finally, a group field theory for this spin foam model is described.

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4

Murgan, Rajan. "Bethe Ansatz and Open Spin-1/2 XXZ Quantum Spin Chain." Scholarly Repository, 2008. http://scholarlyrepository.miami.edu/oa_dissertations/69.

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The open spin-1/2 XXZ quantum spin chain with general integrable boundary terms is a fundamental integrable model. Finding a Bethe Ansatz solution for this model has been a subject of intensive research for many years. Such solutions for other simpler spin chain models have been shown to be essential for calculating various physical quantities, e.g., spectrum, scattering amplitudes, finite size corrections, anomalous dimensions of certain field operators in gauge field theories, etc. The first part of this dissertation focuses on Bethe Ansatz solutions for open spin chains with nondiagonal boundary terms. We present such solutions for some special cases where the Hamiltonians contain two free boundary parameters. The functional relation approach is utilized to solve the models at roots of unity, i.e., for bulk anisotropy values eta = i pi/(p+1) where p is a positive integer. This approach is then used to solve open spin chain with the most general integrable boundary terms with six boundary parameters, also at roots of unity, with no constraint among the boundary parameters. The second part of the dissertation is entirely on applications of the newly obtained Bethe Ansatz solutions. We first analyze the ground state and compute the boundary energy (order 1 correction) for all the cases mentioned above. We extend the analysis to study certain excited states for the two-parameter case. We investigate low-lying excited states with one hole and compute the corresponding Casimir energy (order 1/N correction) and conformal dimensions for these states. These results are later generalized to many-hole states. Finally, we compute the boundary S-matrix for one-hole excitations and show that the scattering amplitudes found correspond to the well known results of Ghoshal and Zamolodchikov for the boundary sine-Gordon model provided certain identifications between the lattice parameters (from the spin chain Hamiltonian) and infrared (IR) parameters (from the boundary sine-Gordon S-matrix) are made.

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5

Liu, Chen. "Variational methods and their applications to frustrated quantum spin models." Thesis, Boston University, 2012. https://hdl.handle.net/2144/32030.

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Thesis (Ph.D.)--Boston University PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. Quantum spin models are useful in many areas of physics, such as strongly correlated materials and quantum phase transitions, or, generally, quantum many-body systems. Most of the models of interest are not analytically solvable. Therefore they are often investigated using computational methods. However, spin models with frustrated interactions are not easily simulated numerically with existing methods, and more effective algorithms are needed. In this thesis, I will cover two areas of quantum spin research: 1. studies of several quantum spin models and 2. development of more efficient computational methods. The discussion of the computational methods and new algorithms is integrated with the physical properties of the models and new results obtained. I study the frustrated S=1/2 J1-J2 model Heisenberg model, the J-Q model, the Ising model with a transverse magnetic field, and a two-orbital spin model describing the magnetic properties of iron pnictides. I will discuss several computational algorithms, including a cluster variational method using mean-field boundary conditions, variational quantum Monte Carlo simulation with clusters-based wave functions, as well as a method I call "optilization" -- an algorithm constructed in order to accelerate the process of optimization with a large number of parameters. I apply it to matrix product states. 2031-01-02

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6

Harada, Kenji. "Numerical Study of Quantum Spin Models by Loop Algorithm." Kyoto University, 1998. http://hdl.handle.net/2433/77874.

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7

Nicotra, Alessandro. "Analytical map between EPRL spin foam models in loop quantum gravity." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23179/.

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Loop Quantum Gravity (LQG) is one of the theoretical frameworks attempting to build a quantum theory of gravitation. Spin Foam theory provides a regularized, background-independent, and Lorentz covariant path integral for the transition amplitudes between LQG kinematical states. The state of the art of the theory is the EPRL model, formulated with the Euclidean and the Lorentzian signatures. They differ by their gauge group structures, which are respectively SO(4,R) and SO(1,3). The first is a compact group: it has finite-dimensional unitary irreducible representations, and the integral on the group manifold is simple. The second is non-compact. Therefore, the computations in the Lorentzian EPRL model are more complicated than in the Euclidean one. The Euclidean model is the preferred choice for physical calculations. Given their similarities it has been so far assumed, as a strong hypothesis, that the results obtained in the Euclidean model also hold for the Lorentzian one. This work's primary goal is to present the main characteristics of the models and a set of prescriptions to map the structure and, at least in a qualitative way, the results obtained in the Euclidean model into the Lorentzian one. Chapter 1 provides an overview of the basic ingredients of the discussion: General Relativity, BF theories and LQG transition amplitudes between quantum states of spacetime. Chapters 2 and 3 are respectively a description of the Euclidean and Lorentzian EPRL models, from the representation theory of their gauge groups to the construction of the EPRL transition amplitudes. Chapter 4 portrays the current state of research in EPRL Spin Foam theory, with a qualitative description of the main results achieved in both models. The main topic of the thesis and my original work is contained in Chapter 5, in which, from a set of prescriptions, the group structure of the Euclidean model is mapped into the Lorentzian one, allowing a comparison between the transition amplitudes.

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8

Shevchenko, Pavel Physics Faculty of Science UNSW. "Quantum Phenomena in Strongly Correlated Electrons Systems." Awarded by:University of New South Wales. Physics, 1999. http://handle.unsw.edu.au/1959.4/32669.

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Quantum phenomena in high-Tc superconductors and dimerized quantum Heisenberg antiferromagnets are studied analytically in this thesis. The implications of the Fermi surface consisting of the disjoint pieces, observed in cuprate superconductors, are considered. It is demonstrated that in this case the g-wave superconducting pairing is closely related to d-wave pairing. The superconductivity in this system can be described in terms of two almost degenerate superconducting condensates. As a result a new spatial scale lg, much larger than the superconducting correlation length x, arises and a new collective excitation corresponding to the relative phase oscillation between condensates, the phason, should exist. The Josephson tunneling for such a two-component system has very special properties. It is shown that the presence of g-wave pairing does not contradict the existing SQUID experimental data on tunneling in the ab-plane. Possible ways to experimentally reveal the g-wave component and the phason in a single tunnel junction, as well as in SQUID experiments, are discussed. The dimerized quantum spin models studied in this thesis include double-layer and alternating chain Heisenberg antiferromagnets. To account for strong correlations between the S=1 elementary excitations (triplets) in the dimerized phase; the analytic Brueckner diagram approach based on a description of the excitations as triplets above a strong-coupling singlet ground state; has been applied. The quasiparticle spectrum is calculated by treating the excitations as a dilute Bose gas with infinite on-site repulsion. Analytical calculations of physical observables are in excellent agreement with numerical data.Results obtained for double layer antiferromagnet near the (zero temperature) quantum critical point coincide with those previously obtained within the nonlinear s model approach Additional singlet (S=0) and triplet (S=1) modes are found as two-particle bound states of the elementary triplets in the Heisenberg chain with frustration.

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9

Sarno, Giorgio. "A numerical approach to spin foam models of quantum gravity." Thesis, Aix-Marseille, 2020. http://www.theses.fr/2020AIXM0231.

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Les modèles de mousse de spin proposent une définition covariante de Lorentz de la dynamique de la gravité quantique en boucle.C'est une approche non-perturbative qui a déjà obtenu un résultat important, reproduire la Relativité Générale discrétisée dans une limite semi-classique. Cependant, la complexité analytique des modèles est telle que des questions clés concernant leur cohérence théorique et leurs prédictions physiques restent ouvertes. Dans cette thèse, j'introduis un cadre systématique pour effectuer des calculs numériques dans ce domaine. La thèse contient une introduction aux théories de mousse de spin d’un point de vue théorique et numérique, en particulier au modèle EPRL. Je présente ensuite quatre des six articles que j'ai publiés au cours de mon doctorat, où le cadre numérique a été utilisé pour étudier des problèmes critiques ouverts dans le domaine. Il s'agit notamment de l'étude numérique du modèle semi-classique limite d'un 4-simplexe, en récupérant son action de Regge et en confirmant des calculs analytiques connus ; une étude des mousses de spin non-simplexes pour offrir un aperçu de la limite du continuum de la théorie ; une nouvelle approche pour étudier les triangulations étendues et leur limite semi-classique. Appliquée à une amplitude de transition particulière, la nouvelle approche m'a permis de retrouver des configurations géométriques compatibles avec des paramètres de bord courbes, et d'argumenter contre un litige important dans la littérature appelé flatness-problem. Ces résultats ouvrent une fenêtre pour les calculs dans les théories de mousse de spin et ils fournissent une nouvelle voie pour aborder leur questions encore non résolues Spin foam models provide a Lorentz-covariant definition of the dynamics of loop quantum gravity. They offer a background-independent and non-perturbative quantization of gravity, and in their semiclassical limit, they are related to discretized General Relativity. However, the analytic complexity of the models is such that key questions concerning their theoretical consistency and physical predictions are still open. In this thesis, I introduce a systematic framework to perform numerical computations in this domain, to go beyond the limitations of the analytical techniques. The thesis contains an introduction to spin foam theories from a theoretical and a numerical standpoint, in particular to the EPRL model. I then present four of the six papers I published during my Ph.D., where the numerical framework was used to study critical open problems in the field. These include the numerical study of the semiclassical limit of a 4-simplex, recovering its Regge action and confirming known analytical computations ; a study of non-simplicial spin foams to offer an insight into the continuum limit of the theory ; a new approach to investigate extended triangulations and their semiclassical limit. Applied to a particular transition amplitude, the new approach allowed me to recover geometrical configurations compatible with curved boundary data, and to argue against an important dispute in the literature referred to as flatness problem. These results open a window for calculations in spin foam theories and they provide a new path to address their still unresolved questions

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10

Erbe, Björn [Verfasser], and John [Akademischer Betreuer] Schliemann. "Central spin models: Quantum integrability and hyperfine induced spin dynamics / Björn Erbe. Betreuer: John Schliemann." Regensburg : Universitätsbibliothek Regensburg, 2011. http://d-nb.info/1022820346/34.

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11

Foxon, Tim. "Discrete models for quantum gravity in three dimensions." Thesis, University of Cambridge, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.338071.

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12

Leseleuc, de kerouara Sylvain de. "Quantum simulation of spin models with assembled arrays of Rydberg atoms." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLO007.

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Des atomes individuels piégés dans des matrices de pinces optiques et excités vers des états de Rydberg forment une plateforme expérimentale prometteuse pour la simulation quantique de modèles de spins. Lors de cette thèse, nous avons d’abord résolu le problème du chargement aléatoire des pièges, seulement 50 % d’entre eux étant chargés avec un atome. Nous avons développé une technique pour préparer des matrices 2D, puis 3D, d’atomes de 87Rb en les déplaçant un par un avec une pince optique mobile contrôlée par ordinateur. Nous avons ensuite réalisé le modèle d’Ising en excitant de manière cohérente les atomes depuis leur état électronique fondamental vers un niveau de Rydberg. Après avoir trouvé un régime optimal où l’interaction dipolaire entre deux atomes de Rydberg se réduit à une énergie de van der Waals, nous avons tenté de préparer adiabatiquement l’état de Néel qui minimise l’énergie d’interaction. Nous avons montré que l’efficacité de préparation étaitlimitée par la décohérence induite par les lasers d’excitation. Nous avons ensuite utilisé un autre régime d’interaction, le couplage dipolaire résonant, pour étudier des modèles de spins de type XY, dont le modèle Su-Schrieffer-Heeger, connu pour sa phase fermionique topologique protégée par une symétrie chirale. Ici, nous avons remplacé les fermions par des particules effectives de type `boson de cœur dur’, ce qui modifie les propriétés de cette phase. Nous avons d’abord retrouvé les propriétés à une particule, comme l’existence d’états de bords à énergie nulle. Nous avons ensuite préparé l’état fondamental à N corps pour un remplissage moitié, et observé sa dégénérescence causée par les états de bords, même en présence d’une perturbation qui lèverait cette dégénérescence dans le cas fermionique. Nous avons expliqué ce résultat par l’existence d’une symétrie plus générale, qui protège la phase bosonique Single atoms trapped in arrays of optical tweezers and excited to Rydberg states are a promising experimental platform for the quantum simulation of spin models. In this thesis, we first solved a long-standing challenge to this approach caused by the random loading of the traps, with only 50% of them filled with single atoms. We have engineered a robust and easy-to-use method to assemble perfectly filled two-dimensional arrays of 87Rb atoms by moving them one by one with a moveable optical tweezers controlled by computer, a technique further enhanced to trap, image and assemble three-dimensional arrays. We then implemented the quantum Ising model by coherently coupling ground-state atoms to a Rydberg level. After finding experimental parameters where the dipole-dipole interaction takes the ideal form of a van der Waals shift, we performed adiabatic preparation of the Néel state. We showed that the coherence time of our excitation lasers limited the efficiency of this technique. We then used a different type of interaction, a resonant dipolar coupling, to implement XY spin models and notably the Su-Schrieffer-Heeger model, known for its fermionic topological phase protected by the chiral symmetry. Here, we used effective hard-core bosons, which modify the properties of the topological phase. We first recovered known properties at the single particle level, such as the existence of localized zero-energy edge-states. Then, preparing the many-body ground state at half-filling, we observed a surprising robustness of its four-fold degeneracy upon applying a perturbation. This result was explained by the existence of a more general symmetry protecting the bosonic phase

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13

Rowlands, Daniel Alexander. "Spectral and dynamical properties of disordered and noisy quantum spin models." Thesis, University of Cambridge, 2019. https://www.repository.cam.ac.uk/handle/1810/284393.

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This thesis, divided into two parts, is concerned with the analysis of spectral and dynamical characteristics of certain quantum spin systems in the presence of either I) quenched disorder, or II) dynamical noise. In the first part, the quantum random energy model (QREM), a mean-field spin glass model with a many-body localisation transition, is studied. In Chapter 2, we attempt a diagrammatic perturbative analysis of the QREM from the ergodic side, proceeding by analogy to the single-particle theory of weak localisation. Whilst we are able to describe diffusion, the analogy breaks down and a description of the onset of localisation in terms of quantum corrections quickly becomes intractable. Some progress is possible by deriving a quantum kinetic equation, namely the relaxation of the one-spin reduced density matrix is determined, but this affords little insight and extension to two-spin quantities is difficult. We change our approach in Chapter 3, studying instead a stroboscopic version of the model using the formalism of quantum graphs. Here, an analytic evaluation of the form factor in the diagonal approximation is possible, which we find to be consistent with the universal random matrix theory (RMT) result in the ergodic regime. In Chapter 4, we replace the QREM's transverse field with a random kinetic term and present a diagrammatic calculation of the average density of states, exact in the large-N limit, and interpret the result in terms of the addition of freely independent random variables. In the second part, we turn our attention to noisy quantum spins. Chapter 5 is concerned with noninteracting spins coupled to a common stochastic field; correlations arising from the common noise relax only due to the spins' differing precession frequencies. Our key result is a mapping of the equation of motion of n-spin correlators onto the (integrable) non-Hermitian Richardson-Gaudin model, enabling exact calculation of the relaxation rate of correlations. The second problem, addressed in Chapter 6, is that of the dynamics of operator moments in a noisy Heisenberg model; qualitatively different behaviour is found depending on whether or not the noise conserves a component of spin. In the case of nonconserving noise, we report that the evolution of the second moment maps onto the Fredrickson-Andersen model - a kinetically constrained model originally introduced to describe the glass transition. This facilitates a rigorous study of operator spreading in a continuous-time model, providing a complementary viewpoint to recent investigations of random unitary circuits.

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14

Dimitrova, Ivana Ljubomirova. "Realizing quantum spin models with ⁷Li atoms in an optical lattice." Thesis, Massachusetts Institute of Technology, 2020. https://hdl.handle.net/1721.1/128327.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, February, 2020 Cataloged from PDF version of thesis. Includes bibliographical references (pages 279-292). Quantum spin Hamiltonians are paradigmatic models, which display different kinds of quantum phase transitions, strongly-correlated and topological ground states, and various regimes of transport. Expanding their significance, many mappings exist between quantum spin models and other systems in different areas of physics, mathematics, and beyond. Even though quantum spin models have been studied extensively, there are still many open questions. Simulating these Hamiltonians with the system of ultracold atoms in optical lattices provides a new perspective with the wide tunability of parameters and the minimal coupling to the environment. The mapping involves using the Mott insulating state of ultracold atoms in optical lattices, where the energy of a second-order tunneling process (superexchange) maps to the parameters of a Heisenberg model. This thesis provides a detailed roadmap for the design and building of such a quantum simulator with ⁷Li atoms in optical lattices. Each step of the process is described, together with the methods and techniques used for the building and the characterization of the physical system. A focus is placed on using the Mott insulator as a starting point for spin physics experiments and, in particular, on the characterization and improvements of the mapping from a density sector description to a spin sector description of the system. Several schemes for implementing and studying spin systems are presented. In particular, the feasibility of implementing the Heisenberg spin-1/2 and spin-1 models in this system is described. The tilted lattice is presented as a tool for studying pure superexchange-driven dynamics and for increasing their timescale by suppressing first order tunneling and the role of number defects. The first measurements and the tuning with this machine of superexchange-driven dynamics over a wide range in the anisotropic Heisenberg spin-1/2 models are presented. Finally, the versatility of the BEC 5 machine is showcased by a study which does not involve an optical lattice. It explores the realization of an exotic quantum phase, a supersolid, in a new way. After many years of building and improvements, the BEC 5 machine emerges as a repeatable and reliable quantum simulator which has a clear scientific agenda of exploring many-body ground states and non-equilibrium dynamics. by Ivana Ljubomirova Dimitrova. Ph. D. Ph.D. Massachusetts Institute of Technology, Department of Physics

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15

Grosse, Harald, Karl-Georg Schlesinger, and grosse@doppler thp univie ac at. "A Suggestion for an Integrability Notion for Two Dimensional Spin." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1015.ps.

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16

Goomanee, Salvish. "Rigorous Approach to Quantum Integrable Models at Finite Temperature." Thesis, Lyon, 2019. http://www.theses.fr/2019LYSEN039/document.

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Cette thèse développe un cadre rigoureux qui permet de démontrer des représentations exactes associées à divers observables de la chaîne XXZ de Heisenberg de spin 1/2 à température finie. Il a était argumenté dans la littérature que l’énergie libre par site ou les longueurs de corrélations admettent des représentations intégrales où les intégrandes sont exprimées en termes de solutions d’équations intégrales non-linéaires. Les dérivations de ces représentations reposaient sur divers conjectures telles que l’existence d’une valeur propre de la matrice de transfert quantique, real, non-dégénérée, de module maximale, de l’échangeabilitée de la limite du volume infinie et du nombre de Trotter à l’infinie, de l’existence et de l’unicité des solutions des equation intégrales non-linéaires auxiliaires et finalement de l’identification des valeurs propers de la matrice de transfert quantiques avec les solutions de l’équations intégrales non-linéaires. Nous démontrons toutes ces conjectures dans le regime de haute température. Nôtre analyse nous permet aussi de démontrer que pour ces température suffisamment élevées, il est possible d’avoir une description d’un certain sous-ensemble de valeurs propres sous-dominante de la matrice de transfert quantique décrite en terme de solutions d’une chaîne de spin-1 de taille finie This thesis develops a rigorous framework allowing one to prove the exact representations for various observables in the XXZ Heisenberg spin-1/2 chain at finite temperature. Previously it has been argued in the literature that the per-site free energy or the correlation lengths admit integral representations whose integrands are expressed in terms of solutions of non-linear integral equations. The derivations of such representations relied on various conjectures such as the existence of a real, non-degenerate, maximal in modulus Eigenvalue of the quantum transfer matrix, the exchangeability of the infinite volume limit and the Trotter number limits, the existence and uniqueness of the solutions to the auxiliary non-linear integral equations and finally the identification of the quantum transfer matrix’s Eigenvalues with solutions to the non-linear integral equation. We rigorously prove all these conjectures in the high temperature regime. Our analysis also allows us to prove that for temperatures high enough, one may describe a certain subset of sub-dominant Eigenvalues of the quantum transfer matrix described in terms of solutions to a spin-1 chain of finite length

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17

Flynn, James S. "A study of two quantum spin models on the body-centred cubic lattice." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0028/MQ36440.pdf.

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18

Davis, Alexander Michael. "Supersymmetry Method for Network Models of Quantum Hall Transitions and Hybrid Structures." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1566157715556164.

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19

Gergs, Anne Cornelie Verfasser], Stefan [Akademischer Betreuer] [Weßel, and Riccardo [Akademischer Betreuer] Mazzarello. "Effective quantum spin models for graphene nanoribbons / Anne Cornelie Gergs ; Stefan Weßel, Riccardo Mazzarello." Aachen : Universitätsbibliothek der RWTH Aachen, 2018. http://d-nb.info/1171906838/34.

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20

Gergs, Anne Cornelie [Verfasser], Stefan [Akademischer Betreuer] Weßel, and Riccardo [Akademischer Betreuer] Mazzarello. "Effective quantum spin models for graphene nanoribbons / Anne Cornelie Gergs ; Stefan Weßel, Riccardo Mazzarello." Aachen : Universitätsbibliothek der RWTH Aachen, 2018. http://d-nb.info/1171906838/34.

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21

Exler, Matthias. "On classical and quantum mechanical energy spectra of finite Heisenberg spin systems." Doctoral thesis, [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=980110440.

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22

Juozapavicius, Ausrius. "Density-Matrix Renormalization-Group Analysis of Kondo and XY models." Doctoral thesis, KTH, Physics, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3260.

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23

Schober, Giulio Albert Heinrich [Verfasser], and Manfred [Akademischer Betreuer] Salmhofer. "Quantum Field Theory of Material Properties: Its Application to Models of Rashba Spin Splitting / Giulio Albert Heinrich Schober ; Betreuer: Manfred Salmhofer." Heidelberg : Universitätsbibliothek Heidelberg, 2016. http://d-nb.info/1180738195/34.

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24

Bidzhiev, Kemal. "Out-of-equilibrium dynamics in a quantum impurity model." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLS352/document.

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Анотація:

Le domaine des problèmes quantiques à N-corps à l'équilibre et hors d'équilibre sont des sujets majeurs de la Physique et de la Physique de la matière condensée en particulier. Les propriétés d'équilibre de nombreux systèmes unidimensionnels en interaction sont bien comprises d'un point de vue théorique, des chaînes de spins aux théories quantiques des champs dans le continue. Ces progrès ont été rendus possibles par le développement de nombreuses techniques puissantes, comme, par exemple, l'ansatz de Bethe, le groupe de renormalisation, la bosonisation, les états produits de matrices ou la théorie des champs invariante conforme. Même si les propriétés à l'équilibre de nombreux modèles soient connues, ceci n'est en général pas suffisant pour décrire leurs comportements hors d'équilibre, et ces derniers restent moins explorés et beaucoup moins bien compris. Les modèles d'impuretés quantiques représentent certains des modèles à N-corps les plus simples. Mais malgré leur apparente simplicité ils peuvent capturer plusieurs phénomènes expérimentaux importants, de l'effet Kondo dans les métaux aux propriétés de transports dans les nanostructures, comme les points quantiques. Dans ce travail nous considérons un modèle d'impureté appelé "modèle de niveau résonnant en interaction" (IRLM). Ce modèle décrit des fermions sans spin se propageant dans deux fils semi-infinis qui sont couplés à un niveau résonant -- appelé point ou impureté quantique -- via un terme de saut et une répulsion Coulombienne. Nous nous intéressons aux situations hors d'équilibre où un courant de particules s'écoule à travers le point quantique, et étudions les propriétés de transport telles que le courant stationnaire (en fonction du voltage), la conductance différentielle, le courant réfléchi, le bruit du courant ou encore l'entropie d'intrication. Nous réalisons des simulations numériques de la dynamique du modèle avec la méthode du groupe de renormalisation de la matrice densité dépendent du temps (tDMRG), qui est basée sur une description des fonctions d'onde en terme d'états produits de matrices. Nous obtenons des résultats de grande précision concernant les courbes courant-voltage ou bruit-voltage de l'IRLM, dans un grand domaine de paramètres du modèle (voltage, force de l'interaction, amplitude de saut vers le dot, etc.). Ces résultats numériques sont analysés à la lumière de résultats exacts de théorie des champs hors d'équilibre qui ont été obtenus pour un modèle similaire à l'IRLM, le modèle de Sine-Gordon avec bord (BSG). Cette analyse est en particulier basée sur l'identification d'une échelle d'énergie Kondo et d'exposants décrivant les régimes de petit et grand voltage. Aux deux points particuliers où les modèles sont connus comme étant équivalents, nos résultats sont en accord parfait avec la solution exacte. En dehors de ces deux points particuliers nous trouvons que les courbes de transport de l'IRLM et du modèle BSG demeurent très proches, ce qui était inattendu et qui reste dans une certaine mesure inexpliqué The fields of in- and out-of-equilibrium quantum many-body systems are major topics in Physics, and in condensed-matter Physics in particular. The equilibrium properties of one-dimensional problems are well studied and understood theoretically for a vast amount of interacting models, from lattice spin chains to quantum fields in a continuum. This progress was allowed by the development of diverse powerful techniques, for instance, Bethe ansatz, renormalization group, bosonization, matrix product states and conformal field theory. Although the equilibrium characteristics of many models are known, this is in general not enough to describe their non-equilibrium behaviors, the latter often remain less explored and much less understood. Quantum impurity models represent some of the simplest many-body problems. But despite their apparent simplicity, they can capture several important experimental phenomena, from the Kondo effect in metals to transport in nanostructures such as point contacts or quantum dots. In this thesis consider a classic impurity model - the interacting resonant level model (IRLM). The model describes spinless fermions in two semi-infinite leads that are coupled to a resonant level -- called quantum dot or impurity -- via weak tunneling and Coulomb repulsion. We are interested in out-of-equilibrium situations where some particle current flows through the dot, and study transport characteristics like the steady current (versus voltage), differential conductance, backscattered current, current noise or the entanglement entropy. We perform extensive state-of-the-art computer simulations of model dynamics with the time-dependent density renormalization group method (tDMRG) which is based on a matrix product state description of the wave functions. We obtain highly accurate results concerning the current-voltage and noise-voltage curves of the IRLM in a wide range parameter of the model (voltage bias, interaction strength, tunneling amplitude to the dot, etc.).These numerical results are analyzed in the light of some exact out-of-equilibrium field-theory results that have been obtained for a model similar to the IRLM, the boundary sine-Gordon model (BSG).This analysis is in particular based on identifying an emerging Kondo energy scale and relevant exponents describing the high- and low- voltage regimes. At the two specific points where the models are known to be equivalent our results agree perfectly with the exact solution. Away from these two points, we find that, within the precision of our simulations, the transport curves of the IRLM and BSG remain very similar, which was not expected and which remains somewhat unexplained

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25

Bondesan, Roberto. "Edge states and supersymmetric sigma models." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2012. http://tel.archives-ouvertes.fr/tel-00808736.

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Une propriété fondamentale de l'effet Hall quantique est la présence des états de bord. Ils résistent á la localisation et sont responsables de la quantification parfaite de la conductance de Hall. La transition entre les plateaux d'effet Hall quantique entier est une transition de délocalisation, qui peut être identifiée comme un point fixe de couplage fort d'un modèle sigma supersymétrique en 1+1-dimensions avec terme topologique theta. La théorie conforme décrivant cette transition présente des caractéristiques inhabituelles telles que la non-unitarité, et a résisté á toute tentative de résolution jusqu'á présent. Dans cette thèse, nous étudions le rôle des états de bord dans les transitions d'effet Hall, en utilisant des discrétisations sur réseau de modèles sigma. Les états de bord correspondent aux conditions aux bord pour les champs des modèles sigma, et peuvent être discrétisés en terme de chaînes de spins quantiques ou de modèles géométriques (de boucles). Pour l'effet Hall de spin, un équivalent de l'effet Hall entier pour le transport de spin (classe C), nos techniques permettent le calcul exact des exposants critiques des théories conformes avec bord décrivant les transitions entre plateaux élevés. Nos prédictions pour la moyenne de la conductance de spin sont validées par des simulations numériques des problèmes de localisation correspondant. Dans cette thèse, envisageant des applications au transport dans les modèles sur réseau des électrons désordonnés en 2+1-dimensions, et aux trempes dans des systèmes quantiques á une dimension, nous avons également développé un nouveau formalisme pour calculer des fonctions de partition de systèmes critiques sur un rectangle. Comme application, nous dérivons des formules de probabilités pour les marches auto-évitantes.

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26

Schäpers, Markus. "Exploring the Frustrated Spin-Chain Compound Linarite by NMR and Thermodynamic Investigations." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-153947.

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Within the last decades low-dimensional frustrated quantum spin systems have attracted great interest in the field of modern research. In these systems a competition of various magnetic interactions takes place, leading to an energetically degenerated magnetic ground state, and thus to the occurrence of exotic, unconventional physical properties at low temperatures. This thesis focuses on the quasi one-dimensional frustrated spin chain system linarite, PbCuSO4(OH)2. In this compound the basic building blocks are CuO4 plaquettes which are connected to each other along one crystallographic direction, analogue to a chain. The frustration in linarite is established due to the competition between the magnetic interactions. The nearest-neighbor magnetic spins are coupled ferromagnetically along the chain via a coupling constant J1, while the next-nearest neighbors are coupled antiferromagnetically via a coupling constant J2. For this configuration it is not possible to satisfy all magnetic couplings simultaneously, hence the system is magnetically frustrated. In this work, comprehensive thermodynamic and nuclear magnetic resonance (NMR) studies demonstrate that linarite is one of the richest and most fascinating compounds in the class of low-dimensional frustrated magnets. By means of susceptibility, magnetization, specific heat, magnetocaloric effect, magnetostriction, and thermal-expansion measurements a rich magnetic phase diagram could be mapped out below a temperature of 2.8 K. The phase diagram contains five different magnetic regions/phases for an external magnetic field pointing along the chain direction. Based on the thermodynamic studies it was possible to calculate the exchange integrals within the frustrated J1-J2 model and extensions of it by using various theoretical approaches. The magnetic microscopic nature of the different long-range magnetic phases present in linarite were investigated by NMR measurements and by collaborative neutron scattering experiments. The ground state (phase I) is identified as an incommensurate elliptical helical structure. Via a theoretical modelling the 1H-NMR spectrum of the ground state could be explained, revealing a rearrangement of the zero-field structure in an external magnetic field of 2.0 T used for the NMR studies. By further increasing the external field the system undergoes a complex spin flop transition in two steps (phase I - phase III - phase IV). In phase III a phase separation takes place where one part of the spins form a circular spiral structure while the remaining fraction form a simple antiferromagnetic structure. In phase IV the remaining circular spiral structure vanishes, so that all spins collectively form the antiferromagnetic collinear phase. The most peculiar physical properties studied in this thesis take place in region V at high fields, showing only tiny features in the thermodynamic properties. The magnetic spins in region V form a sine-wave modulated spin-density structure as identified via NMR and neutron investigations. It is discussed whether region V is related to a multipolar phase or if the spin-density wave structure could possibly coexist with such a phase.

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27

Tschirhart, Hugo. "From two Algebraic Bethe Ansätze to the dynamics of Dicke-Jaynes-Cummings-Gaudin quantum integrable models through eigenvalue-based determinants." Thesis, Université de Lorraine, 2017. http://www.theses.fr/2017LORR0098/document.

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Le travail présenté dans cette thèse est inspiré de précédents résultats sur les modèles de Gaudin ne contenant que des spins-1/2 (ces modèles sont intégrables) qui, par un changement de variable dans les équations de Bethe algébriques, parviennent à simplifier le traitement numérique de ces modèles. Cette optimisation numérique s'effectue par l'intermédiaire d'une construction en déterminant, ne dépendant que des variables précédemment mentionnées, pour chaque produit scalaire intervenant dans l'expression de la moyenne d'une observable à un temps donné. En montrant qu'il est possible d'utiliser la méthode du Quantum Inverse Scattering Method (QISM), même dans un cas où l'état du vide n'est pas état propre de la matrice de transfert, les résultats précédents concernant uniquement des spins-1/2 sont généralisés à des modèles contenant en plus une interaction spin-boson. De fait, cette généralisation a ouvert plusieurs voies de recherche possibles. Premièrement, il est montré qu'il est possible de continuer à généraliser l'utilisation de déterminants pour des modèles de spins décrivant l'interaction d'un spin de norme arbitraire avec des spins-1/2. La méthode permettant d'obtenir la construction des expressions explicites de ces déterminants est donnée. On peut également pousser la généralisation à d'autres modèles de Gaudin dont l'état du vide n'est pas état propre de la matrice de transfert. C'est ce que nous avons fait pour des spins-1/2 en interaction avec un champ magnétique dont l'orientation est arbitraire. Enfin, un traitement numérique de ces systèmes de spins-1/2 interagissant avec un mode bosonique est présenté. L'évolution temporelle de l'occupation bosonique et de l'aimantation locale des spins est ainsi étudiée selon deux Hamiltoniens différents, l'Hamiltonien de Tavis-Cummings et un Hamiltonien type spin central. Cette étude nous apprend que la dynamique de ces systèmes, qui relaxent d'un état initial vers un état stationnaire, conduit à un état superradiant lorsque l'état initial choisi y est favorable The work presented in this thesis was inspired by precedent results on the Gaudin models (which are integrable) for spins-1/2 only which, by a change of variables in the algebraic Bethe equations, manage to considerably simplify the numerical treatment of such models. This numerical optimisation is carried out by the construction of determinants, only depending on the previously mentioned variables, for every scalar products appearing in the expression of the mean value of an observable of interest at a given time. By showing it is possible to use the Quantum Inverse Scattering Method (QISM), even when the vacuum state is not eigenstate of the transfer matrix, the previous results concerning spins-1/2 only are generalised to models including an additional spin-boson interaction. De facto, this generalisation opened different possible paths of research. First of all, we show that it is possible to further generalise the use of determinants for spin models describing the interaction of one spin of arbitrary norm with many spins-1/2. We give the method leading to the explicit construction of determinants’ expressions. Moreover, we can extend this work to other Gaudin models where the vacuum state is not an eigenstate of the transfer matrix. We did this work for spins-1/2 interacting with an arbitrarily oriented magnetic field. Finally, a numerical treatment of systems describing the interaction of many spins-1/2 with a single bosonic mode is presented. We study the time evolution of bosonic occupation and of local magnetisation for two different Hamiltonians, the Tavis-Cummings Hamiltonian and a central spin Hamiltonian. We learn that the dynamics of these systems, relaxing from an initial state to a stationary state, leads to a superradiant-like state for certain initial states

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28

Stephan, Jean-Marie. "Intrication dans des systèmes quantiques à basse dimension." Thesis, Paris 11, 2011. http://www.theses.fr/2011PA112308.

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On a compris ces dernières années que certaines mesures d'intrications sont un outil efficace pour la compréhension et la caractérisation de phases nouvelles et exotiques de la matière, en particulier lorsque les méthodes traditionnelles basées sur l'identification d'un paramètre d'ordre sont insuffisantes. Cette thèse porte sur l'étude de quelques systèmes quantiques à basse dimension où un telle approche s'avère fructueuse. Parmi ces mesures, l'entropie d'intrication, définie via une bipartition du système quantique, est probablement la plus populaire, surtout à une dimension. Celle-ci est habituellement très difficile à calculer en dimension supérieure, mais nous montrons ici que le calcul se simplifie drastiquement pour une classe particulière de fonctions d'ondes, nommées d'après Rokhsar et Kivelson. L'entropie d'intrication peut en effet s'exprimer comme une entropie de Shannon relative à la distribution de probabilité générée par les composantes de la fonction d'onde du fondamental d'un autre système quantique, cette fois-ci unidimensionnel. Cette réduction dimensionnelle nous permet d'étudier l'entropie aussi bien par des méthodes numériques (fermions libres, diagonalisations exactes, ...) qu'analytiques (théories conformes). Nous argumentons aussi que cette approche permet d'accéder facilement à certaines caractéristiques subtiles et universelles d'une fonction d'onde donnée en général.Une autre partie de cette thèse est consacrée aux trempes quantiques locales dans des systèmes critiques unidimensionnels. Nous insisterons particulièrement sur une quantité appelée écho de Loschmidt, qui est le recouvrement entre la fonction d'onde avant la trempe et la fonction d'onde à temps t après la trempe. En exploitant la commensurabilité du spectre de la théorie conforme, nous montrons que l'évolution temporelle doit être périodique, et peut même être souvent obtenue analytiquement. Inspiré par ces résultats, nous étudions aussi la contribution de fréquence nulle à l'écho de Loschmidt après la trempe. Celle-ci s'exprime comme un simple produit scalaire -- que nous nommons fidélité bipartie -- et est une quantité intéressante en elle-même. Malgré sa simplicité, son comportement se trouve être très similaire à celui de l'entropie d'intrication. Pour un système critique unidimensionnel en particulier, notre fidélité décroît algébriquement avec la taille du système, un comportement rappelant la célèbre catastrophe d'Anderson. L'exposant est universel et relié à la charge centrale de la théorie conforme sous-jacente In recent years, it has been understood that entanglement measures can be useful tools for the understanding and characterization of new and exotic phases of matter, especially when the study of order parameters alone proves insufficient. This thesis is devoted to the study of a few low-dimensional quantum systems where this is the case. Among these measures, the entanglement entropy, defined through a bipartition of the quantum system, has been perhaps one of the most heavily studied, especially in one dimension. Such a quantity is usually very difficult to compute in dimension larger than one, but we show that for a particular class of wave functions, named after Rokhsar and Kivelson, the entanglement entropy of an infinite cylinder cut into two parts simplifies considerably. It can be expressed as the Shannon entropy of the probability distribution resulting from the ground-state wave function of a one-dimensional quantum system. This dimensional reduction allows for a detailed numerical study (free fermion, exact diagonalizations, \ldots) as well as an analytic treatment, using conformal field theory (CFT) techniques. We also argue that this approach can give an easy access to some refined universal features of a given wave function in general.Another part of this thesis deals with the study of local quantum quenches in one-dimensional critical systems. The emphasis is put on the Loschmidt echo, the overlap between the wave function before the quench and the wave function at time t after the quench. Because of the commensurability of the CFT spectrum, the time evolution turns out to be periodic, and can be obtained analytically in various cases. Inspired by these results, we also study the zero-frequency contribution to the Loschmidt echo after such a quench. It can be expressed as a simple overlap -- which we name bipartite fidelity -- and can be studied in its own right. We show that despite its simple definition, it mimics the behavior of the entanglement entropy very well. In particular when the one-dimensional system is critical, this fidelity decays algebraically with the system size, reminiscent of Anderson's celebrated orthogonality catastrophe. The exponent is universal and related to the central charge of the underlying CFT

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29

Joshi, Darshan Gajanan. "Magnetic quantum phase transitions: 1/d expansion, bond-operator theory, and coupled-dimer magnets." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-198634.

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In the study of strongly interacting condensed-matter systems controlled microscopic theories hold a key position. Spin-wave theory, large-N expansion, and $epsilon$-expansion are some of the few successful cornerstones. In this doctoral thesis work, we have developed a novel large-$d$ expansion method, $d$ being the spatial dimension, to study model Hamiltonians hosting a quantum phase transition between a paramagnet and a magnetically ordered phase. A highlight of this technique is that it can consistently describe the entire phase diagram of the above mentioned models, including the quantum critical point. Note that most analytical techniques either efficiently describe only one of the phases or suffer from divergences near the critical point. The idea of large-$d$ formalism is that in this limit, non-local fluctuations become unimportant and that a suitable product state delivers exact expectation values for local observables, with corrections being suppressed in powers of $1/d$. It turns out that, due to momentum summation properties of the interaction structure factor, all diagrams are suppressed in powers of $1/d$ leading to an analytic expansion. We have demonstrated this method in two important systems namely, the coupled-dimer magnets and the transverse-field Ising model. Coupled-dimer magnets are Heisenberg spin systems with two spins, coupled by intra-dimer antiferromagnetic interaction, per crystallographic unit cell (dimer). In turn, spins from neighboring dimers interact via some inter-dimer interaction. A quantum paramagnet is realized for a dominant intra-dimer interaction, while a magnetically ordered phase exists for a dominant (or of the same order as intra-dimer interaction) inter-dimer interaction. These two phases are connected by a quantum phase transition, which is in the Heisenberg O(3) universality class. Microscopic analytical theories to study such systems have been restricted to either only one of the phases or involve uncontrolled approximations. Using a non-linear bond-operator theory for spins with S=$1/2$, we have calculated the $1/d$ expansion of static and dynamic observables for coupled dimers on a hypercubic lattice at zero temperature. Analyticity of the $1/d$ expansion, even at the critical point, is ensured by correctly identifying suitable observables using the mean-field critical exponents. This method yields gapless excitation modes in the continuous symmetry broken phase, as required by Goldstone\'s theorem. In appropriate limits, our results match with perturbation expansion in small ratio of inter-dimer and intra-dimer coupling, performed using continuous unitary transformations, as well as the spin-wave theory for spin-$1/2$ in arbitrary dimensions. We also discuss the Brueckner approach, which relies on small quasiparticle density, and derive the same $1/d$ expansion for the dispersion relation in the disordered phase. Another success of our work is in describing the amplitude (Higgs) mode in coupled-dimer magnets. Our novel method establishes the popular bond-operator theory as a controlled approach. In $d=2$, the results from our calculations are in qualitative agreement with the quantum Monte Carlo study of the square-lattice bilayer Heisenberg AF spin-$1/2$ model. In particular, our results are useful to identify the amplitude (Higgs) mode in the QMC data. The ideas of large-$d$ are also successfully applied to the transverse-field Ising model on a hypercubic lattice. Similar to bond operators, we have introduced auxiliary Bosonsic operators to set up our method in this case. We have also discussed briefly the bilayer Kitaev model, constructed by antiferromagnetically coupling two layers of the Kitaev model on a honeycomb lattice. In this case, we investigate the dimer quantum paramagnetic phase, realized in the strong inter-layer coupling limit. Using bond-operator theory, we calculate the mode dispersion in this phase, within the harmonic approximation. We also conjecture a zero-temperature phase diagram for this model.

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30

Carrozza, Sylvain. "Tensorial methods and renormalization in Group Field Theories." Thesis, Paris 11, 2013. http://www.theses.fr/2013PA112147/document.

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Cette thèse présente une étude détaillée de la structure de théories appelées GFT ("Group Field Theory" en anglais),à travers le prisme de la renormalisation. Ce sont des théories des champs issues de divers travaux en gravité quantique, parmi lesquels la gravité quantique à boucles et les modèles de matrices ou de tenseurs. Elles sont interprétées comme desmodèles d'espaces-temps quantiques, dans le sens où elles génèrent des amplitudes de Feynman indexées par des triangulations,qui interpolent les états spatiaux de la gravité quantique à boucles. Afin d'établir ces modèles comme des théories deschamps rigoureusement définies, puis de comprendre leurs conséquences dans l'infrarouge, il est primordial de comprendre leur renormalisation. C'est à cette tâche que cette thèse s'attèle, grâce à des méthodes tensorielles développées récemment,et dans deux directions complémentaires. Premièrement, de nouveaux résultats sur l'expansion asymptotique (en le cut-off) des modèles colorés de Boulatov-Ooguri sont démontrés, donnant accès à un régime non-perturbatif dans lequel une infinité de degrés de liberté contribue. Secondement, un formalisme général pour la renormalisation des GFTs dites tensorielles (TGFTs) et avec invariance de jauge est mis au point. Parmi ces théories, une TGFT en trois dimensions et basée sur le groupe de jauge SU(2) se révèle être juste renormalisable, ce qui ouvre la voie à l'application de ce formalisme à la gravité quantique In this thesis, we study the structure of Group Field Theories (GFTs) from the point of view of renormalization theory.Such quantum field theories are found in approaches to quantum gravity related to Loop Quantum Gravity (LQG) on the one hand,and to matrix models and tensor models on the other hand. They model quantum space-time, in the sense that their Feynman amplitudes label triangulations, which can be understood as transition amplitudes between LQG spin network states. The question of renormalizability is crucial if one wants to establish interesting GFTs as well-defined (perturbative) quantum field theories, and in a second step connect them to known infrared gravitational physics. Relying on recently developed tensorial tools, this thesis explores the GFT formalism in two complementary directions. First, new results on the large cut-off expansion of the colored Boulatov-Ooguri models allow to explore further a non-perturbative regime in which infinitely many degrees of freedom contribute. The second set of results provide a new rigorous framework for the renormalization of so-called Tensorial GFTs (TGFTs) with gauge invariance condition. In particular, a non-trivial 3d TGFT with gauge group SU(2) is proven just-renormalizable at the perturbative level, hence opening the way to applications of the formalism to (3d Euclidean) quantum gravity

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31

Chakhmakhchyan, Levon. "Entangled states and coherent interaction in resonant media." Thesis, Dijon, 2014. http://www.theses.fr/2014DIJOS026/document.

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Nous analysons les caractéristiques d'intrication de quelques matériaux à l'état solide ainsi que des systèmes particuliers d'atomes et de champs en interaction. Une étude détaillée de la riche structure de phase des modèles de spins de basse dimension, décrivant le minéral naturel d'azurite et les composés de coordination à base de cuivre, a révélé des régimes à comportement d'intrication des plus robustes. En utilisant l'approche des systèmes dynamiques, la structure de phase de certains modèles classiques en réseaux hiérarchiques (récursifs) a aussi été étudiée et, pour la première fois, la transition entre régime chaotique et régime périodique au moyen de la bifurcation tangente a été détectée.Nous présentons une description détaillée des propriétés d'intrication de trois atomes piégés dans la limite dispersive. Une relativement simple accordabilité de la force atomique d'interaction de ce système et son étroite relation aux problèmes de frustration magnétique est démontrée. Les effets de propagation de pulses laser intenses dans un système atomique de type [lambda] avec des forces d'oscillateurs différentes sont analysés. Les résultats obtenus sont d'extrême importance dans des problèmes d'information quantique, comme par exemple, dans l'analyse du mécanisme de transfert de population dans des milieux ayant les propriétés définies ci-avant. Enfin, nous avons analysé les effets dissipatifs dans un protocole de distillation de l'intrication à variable continue récemment proposé. Malgré des contraintes additionnelles sur les paramètres du protocole, il est encore possible d'implémenter ce schéma de distillation évoqué ci-avant dans les technologies émergentes The entanglement features of some solid state materials, as well as of particular systems of interacting atoms and fields are analyzed. A detailed investigation of the rich phase structure of low dimensional spin models, describing the natural mineral azurite and copper based coordination compounds, has revealed regimes with the most robust entanglement behavior. Using the dynamical system approach, the phase structure of some classical models on hierarchical (recursive) lattices has been also studied and, for the first time, the transition between chaotic and periodic regimes by means of tangent bifurcation has been detected.A detailed description of entanglement properties of three atoms trapped in a cavity within the dispersive limit is presented. A relatively simple tunability of the atomic interaction strength of the above system and its close relation to the problems of frustrated magnetism is shown. Furthermore, the propagation effects of two intense laser pulses in a medium of [lambda] atoms with unequal oscillator strengths are investigated. Obtained results are crucial in some problems of quantum information theory, as, e.g., in the analysis of population transfer mechanism in media possessing the above properties. Finally, the dissipation effects in a recently proposed compact continuous-variable entanglement distillation protocol have been analyzed. Despite additional constraints on the parameters of the protocol, the discussed entanglement distillation scheme in quantum memories is still possible to implement within emerging technologies

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32

Liu, Yi. "Dynamics, Synchronization and Spin Squeezing in a Two-Spin Model." Thesis, Paris 11, 2013. http://www.theses.fr/2013PA112216.

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Cette thèse se concentre sur la dynamique d'un système atomique froid qui se composede deux états internes d'atomes piégés dans un potentiel magnétique . La motivation decette thèse est une série d'expériences sur ce système réalisées en 2010, où un grandtemps de cohérence surprenante entre les deux états internes ont été observés. Cephénomène a été expliqué par la théorie cinétique qui a utilisé une approche de champmoyen. Dans cette thèse, nous essayons d'utiliser une approche différente et étudier leseffets de corrélations quantiques dans la dynamique du système. De plus, nous sommeségalement intéressés au phénomène de compression de spin qui est la redistribution desfluctuations quantiques dans le système de spin. Afin d'étudier les effets des corrélationsquantiques, nous proposons un modèle simplifié qui divise les atomes froids en deuxgroupes en fonction de leurs énergies de mouvement orbital dans le potentiel de piégeageet traitons chaque groupe comme un macro-spin. Les principaux ingrédients de ce modèlesont l'inhomogénéité du champ externe qui déphase les deux macro-spins et l'interactiond'échange entre les deux macro-spins, qui imite l'effet de rotation des spins identiques(ISRE), avec la condition initiale que les deux spins sont parallèle dans le plan transversaldu champ externe. Ensuite, nous étudions la dynamique du système classique où ladynamique ne dépendent pas de la taille des spins et une transition de synchronisation esttrouvée lorsque l'interaction d'échange est plus grande que le seuil , la moitié de l'inhomogénéité du champ externe. Une analyse de l'espace de phase révèle que cettetransition de synchronisation est liée à une transition de bifurcation et de la conditioninitiale. Ensuite, la dynamique quantique est étudiée où la taille de spin joue un rôleimportant dans la dynamique. Il n'y a pas de transition de synchronisation dans lessystèmes quantiques et du comportement dynamique très riche est trouvée. Dans ladynamique quantique , plusieurs échelles de temps caractéristiques apparaissent commela taille de spin augmente, ce qui est d'origine quantique. Ces échelles de temps dépendde la taille de spin et tous deviennent infinies lorsque la taille de spin est infinie. De cettefaçon, la limite classique est récupéré. Basé sur l’intensité de l'interaction d'échange ,deux modèles effectifs sont proposés pour calculer les échelles du temps quantiques lesplus petites, ce qui coïncide bien avec les résultats numériques. La compression de spinest également étudié avec ces modèles effectifs This thesis focuses on the dynamics of a cold atomic system which consists of two internalstates of atoms trapped in a magnetic trapping potential. The motivation of this thesis is aseries of experiments on such system carried out in 2010, where a surprising longcoherence time between the two internal states were observed. This phenomenon wasexplained by the kinetic theory which has used a mean-field approach. In this thesis, wetry to use a different approach and study the effects of quantum correlations in thedynamics of the system. In addition to that, we are also interested in the phenomenon ofspin squeezing which is the redistribution of quantum fluctuations in the spin system. Inorder to study the effects of the quantum correlations, we propose a simplified which splitsthe cold atoms into two groups based on their orbital movement energies in the trappingpotential and treat each group as a macro-spin. The main ingredients in this model are theinhomogeneity of the external field which dephases the two macro-spins and theexchange interaction between the two macro-spins, which mimics the identical spinrotation effect (ISRE), with the initial condition that the two spins lie parallel in thetransverse plane of the external field. Then we study the classical dynamics of the systemwhere the dynamics do not depend on the size of the spins and a synchronizationtransition is found when the exchange interaction is larger than the threshold, the half ofthe inhomogeneity of the external field. A phase space analysis reveals that thissynchronization transition is related to a bifurcation transition and the initial condition. Thenthe quantum dynamics is studied where the spin size plays an important role in thedynamics. There is no synchronization transition in the quantum systems and very richdynamical behavior is found. In the quantum dynamics, many characteristic time scalesemerge as the size of spin is increased, which are of quantum origin. These time scales isdependent of the spin size and all become infinite when the size of spin is infinite. In theway, the classical limit is recovered. Based on the strength of the exchange interaction,two effective models are proposed to calculate the smallest quantum characteristic timescales, which give very good agreement with the numerical results. Spin squeezing is alsostudied with these effective models

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Meier, Hannes. "Phase transitions in novel superfluids and systems with correlated disorder." Doctoral thesis, KTH, Statistisk fysik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-160929.

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Condensed matter systems undergoing phase transitions rarely allow exact solutions. The presence of disorder renders the situation even worse but collective Monte Carlo methods and parallel algorithms allow numerical descriptions. This thesis considers classical phase transitions in disordered spin systems in general and in effective models of superfluids with disorder and novel interactions in particular. Quantum phase transitions are considered via a quantum to classical mapping. Central questions are if the presence of defects changes universal properties and what qualitative implications follow for experiments. Common to the cases considered is that the disorder maps out correlated structures. All results are obtained using large-scale Monte Carlo simulations of effective models capturing the relevant degrees of freedom at the transition. Considering a model system for superflow aided by a defect network, we find that the onset properties are significantly altered compared to the $\lambda$-transition in $^{4}$He. This has qualitative implications on expected experimental signatures in a defect supersolid scenario. For the Bose glass to superfluid quantum phase transition in 2D we determine the quantum correlation time by an anisotropic finite size scaling approach. Without a priori assumptions on critical parameters, we find the critical exponent $z=1.8 \pm 0.05$ contradicting the long standing result $z=d$. Using a 3D effective model for multi-band type-1.5 superconductors we find that these systems possibly feature a strong first order vortex-driven phase transition. Despite its short-range nature details of the interaction are shown to play an important role. Phase transitions in disordered spin models exposed to correlated defect structures obtained via rapid quenches of critical loop and spin models are investigated. On long length scales the correlations are shown to decay algebraically. The decay exponents are expressed through known critical exponents of the disorder generating models. For cases where the disorder correlations imply the existence of a new long-range-disorder fixed point we determine the critical exponents of the disordered systems via finite size scaling methods of Monte Carlo data and find good agreement with theoretical expectations. QC 20150306

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Asghar, Zahid Bin. "Quantum spin structures and phase separation in the Hubbard model." Thesis, Loughborough University, 2001. https://dspace.lboro.ac.uk/2134/34512.

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In this thesis we focus on a systematic study of the ground state of the one-dimensional one-band Hubbard model in the Hartree–Fock approximation. Phases with non-uniform charge density and states with coexisting phases separated by a domain wall are included in the study. We calculate the full Hartree–Fock phase diagram for uniform and non-uniform phases, and we show that at particular electron densities the uniform phase is unstable to phase separation. Supercell calculations are carried out, and we use the computational minimisation procedure to calculate the Hartree–Fock energies for the self-consistent spin configurations.

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Vernier, Eric. "Non compact conformal field theories in statistical mechanics." Thesis, Paris, Ecole normale supérieure, 2015. http://www.theses.fr/2015ENSU0005/document.

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Les comportements critiques des systèmes de mécanique statistique en 2 dimensions ou de mécanique quantique en 1+1 dimensions, ainsi que certains aspects des systèmes sans interactions en 2+1 dimensions, sont efficacement décrits par les méthodes de la théorie des champs conforme et de l'intégrabilité, dont le développement a été spectaculaire au cours des 40 dernières années. Plusieurs problèmes résistent cependant toujours à une compréhension exacte, parmi lesquels celui de la transition entre plateaux dans l'Effet Hall Quantique Entier. La raison principale en est que de tels problèmes sont généralement associés à des théories non unitaires, ou théories conformes logarithmiques, dont la classification se révèle être d'une grande difficulté mathématique. Se tournant vers la recherche de modèles discrets (chaînes de spins, modèles sur réseau), dans l'espoir en particulier d'en trouver des représentations en termes de modèles exactement solubles (intégrables), on se heurte à la deuxième difficulté représentée par le fait que les théories associées sont la plupart du temps non compactes, ou en d'autres termes qu'elles donnent lieu à un continuum d'exposants critiques. En effet, le lien entre modèles discrets et théories des champs non compactes est à ce jour loin d'être compris, en particulier il a longtemps été cru que de telles théories ne pouvaient pas émerger comme limites continues de modèles discrets construits à partir d'un ensemble compact de degrés de libertés, par ailleurs les seuls qui donnent a accès à une construction systématique de solutions exactes.Dans cette thèse, on montre que le monde des modèles discrets compacts ayant une limite continue non compacte est en fait beaucoup plus grand que ce que les quelques exemples connus jusqu'ici auraient pu laisser suspecter. Plus précisément, on y présente une solution exacte par ansatz de Bethe d'une famille infinie de modèles(les modèles $a_n^{(2)}$, ainsi que quelques résultats sur les modèles $b_n^{(1)}$, où il est observé que tous ces modèles sont décrits dans un certain régime par des théories conformes non compactes. Parmi ces modèles, certains jouent un rôle important dans la description de phénomènes physiques, parmi lesquels la description de polymères en deux dimensions avec des interactions attractives et des modèles de boucles impliqués dans l'étude de modèles de Potts couplés ou dans une tentative de description de la transition entre plateaux dans l'Effet Hall par un modèle géométrique compact.On montre que l'existence insoupçonnéede limite continues non compacts pour de tels modèles peut avoir d'importantes conséquences pratiques, par exemple dans l'estimation numérique d'exposants critiques ou dans le résultats de simulations de Monte Carlo. Nos résultats sont appliqués à une meilleure compréhension de la transition theta décrivant l'effondrement des polymères en deux dimensions, et des perspectives pour une potentielle compréhension de la transition entre plateaux en termes de modèles sur réseaux sont présentées The critical points of statistical mechanical systems in 2 dimensions or quantum mechanical systems in 1+1 dimensions (this also includes non interacting systems in 2+1 dimensions) are effciently tackled by the exact methods of conformal fieldtheory (CFT) and integrability, which have witnessed a spectacular progress during the past 40 years. Several problems have however escaped an exact understanding so far, among which the plateau transition in the Integer Quantum Hall Effect,the main reason for this being that such problems are usually associated with non unitary, logarithmic conformal field theories, the tentative classification of which leading to formidable mathematical dificulties. Turning to a lattice approach, andin particular to the quest for integrable, exactly sovable representatives of these problems, one hits the second dificulty that the associated CFTs are usually of the non compact type, or in other terms that they involve a continuum of criticalexponents. The connection between non compact field theories and lattice models or spin chains is indeed not very clear, and in particular it has long been believed that the former could not arise as the continuum limit of discrete models built out of acompact set of degrees of freedom, which are the only ones allowing for a systematic construction of exact solutions.In this thesis, we show that the world of compact lattice models/spin chains with a non compact continuum limit is much bigger than what could be expected from the few particular examples known up to this date. More precisely we propose an exact Bethe ansatz solution of an infinite family of models (the so-called $a_n^{(2)}$ models, as well as some results on the $b_n^{(1)}$ models), and show that all of these models allow for a regime described by a non compact CFT. Such models include cases ofgreat physical relevance, among which a model for two-dimensional polymers with attractive interactions and loop models involved in the description of coupled Potts models or in a tentative description of the quantum Hall plateau transition by somecompact geometrical truncation. We show that the existence of an unsuspected non compact continuum limit for such models can have dramatic practical effects, for instance on the output of numerical determination of the critical exponents or ofMonte-Carlo simulations. We put our results to use for a better understanding of the controversial theta transition describing the collapse of polymers in two dimensions, and draw perspectives on a possible understanding of the quantum Hall plateautransition by the lattice approach

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Lienhard, Vincent. "Physique quantique expérimentale à N corps dans des matrices d'atomes de Rydberg. Des modèles de spins à la matière topologique." Thesis, Université Paris-Saclay (ComUE), 2019. https://pastel.archives-ouvertes.fr/tel-02949007.

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Des atomes individuels piégés dans des matrices de pinces optiques et excités vers des états de Rydberg forment une plateforme expérimentale performante pour la simulation quantique de problèmes à N corps, comme le confirment les récents progrès dans le domaine. Lors de cette thèse, nous avons d’abord montré la production de matrices de pinces optiques, toutes chargées par des atomes uniques dans leur état fondamental. Notre technique de piégeage a été étendue au cas des atomes de Rydberg. Ces derniers sont chassés des zones de haute intensité par la force pondéromotrice. Par conséquent, nous avons créé par holographie des zones sombres entourés de lumière, pour les confiner. Nous avons aussi étudié les corrélations entre spins dans le cas des Hamiltoniens d’Ising ou XY, en utilisant le régime d’interaction de van der Waals ou dipolaire résonnant. Lors de notre étude du modèle d’Ising, nous avons observé l’apparition de corrélations antiferromagnétiques au cours d’une variation temporelle de l’Hamiltonien, mettant en évidence une vitesse effective pour la propagation des corrélations, ainsi qu’un mécanisme caractéristique de croissance site-à-site. Pour le modèle XY, nous avons montré la préparation d’un nombre contrôlé d’excitations de spin, ainsi que la production de chaînes ferromagnétiques, ou d’un ensemble de chaînes ferromagnétiques anti-alignées deux à deux. Enfin, nous avons utilisé d’autres termes d’échange, présents dans l’interaction dipolaire, pour créer des amplitudes de saut complexe pour une particule effective. Cette utilisation a conduit à l’apparition d’un champ de jauge artificiel, dont l’effet a été mesuré sur un système minimal composé de trois atomes, et ouvre la voie à l’observation d’états de bords chiraux, caractéristiques des isolants topologiques Rydberg-based platforms, involving single atoms trapped in arrays of optical tweezers and excited to Rydberg states, have recently proven attractive to perform quantum simulation of many-body physics. In this thesis, we first demonstrated the generation of arrays of optical tweezers fully loaded by single ground-state atoms. The trapping technique was then extended for Rydberg atoms. The latest are repelled from high-intensity regions via the ponderomotive force, so we created holographically dark regions surrounded by light to confine them. We also studied spin-spin correlations in artificial Ising or XY magnets, engineered by using either the van der Waals or the resonant dipolar coupling between Rydberg atoms. In the Ising case, we observed the growth of antiferromagnetic correlations during a dynamical tuning of the Hamiltonian, revealing an effective velocity for the spreading of correlations, and a typical site to site build-up mechanism. In the XY case, we demonstrated the preparation of a controlled number of spin excitations, and the generation of 1D XY ferromagnets and a 2D stripy order phase (ferromagnetic chains anti-aligned with respect to each other). Finally, we used additional exchange terms of the dipole-dipole interaction to engineer complex hopping amplitudes for an effective particle. This resulted in the emergence of an artificial gauge field, characterized on a minimal three-atom system, and opens the way to the observation of chiral edge states, a signature of topological insulators

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Rosa, Priscila Ferrari Silveira 1988. "Dinâmica quântica de estados de impurezas em cadeias de spin." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/277877.

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Orientador: Guillermo Gerardo Cabrera Oyarzún Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física "Gleb Wataghin" Made available in DSpace on 2018-08-16T15:57:09Z (GMT). No. of bitstreams: 1 Rosa_PriscilaFerrariSilveira_M.pdf: 3441309 bytes, checksum: ac0fe3faa7642e9a7ef8330049e33761 (MD5) Previous issue date: 2010 Resumo: A descrição da dinâmica quântica de sistemas de muitos corpos é um ingrediente chave para a computação quântica. No presente projeto, propomos o estudo da dinâmica em cadeias finitas de spin 1/2 na presença de impurezas ou defeitos. O modelo adotado será o de Ising quântico com campo transverso, do qual é possível obter o espectro de forma exata na presença de uma impureza. A dinâmica do sistema é movida exclusivamente por flutuações quânticas, cuja origem é o Princípio da Incerteza. Investigamos a relaxação de estados iniciais caracterizados por uma magnetização espacialmente não homogênea e que não possuam hipóteses sobre a proximidade com o estado de equilíbrio. Dessa forma, a matriz densidade inicial será dependente apenas de uma única coordenada espacial. A investigação então é realizada através da grandeza de interesse, a saber, a evolução temporal do valor médio das componentes de Fourier da magnetização, (SzQ)t. Soluções exatas, tanto analíticas quanto numéricas, são obtidas. Um dos objetivos iniciais deste trabalho consiste na busca de processos de relaxação lentos. Para os casos de solução analítica (impurezas periódica e antiperiódica) observamos relaxações oscilatórias e amortecidas por uma lei de potência no tempo do tipo (t/tQ)-vQ, onde tQ e vQ são dois parâmetros livres e Q é o número de onda associado a cada componente de Fourier. Há uma criticalidade no expoente vQ, o qual muda de 3/2 para 1/2 para certos valores de Q críticos. Por outro lado, para os casos de solução numérica (impurezas arbitrárias), os processos de relaxação são distintos daqueles citados acima. Os estados iniciais analisados são do tipo produto direto ferromagnético com um único spin virado, próximo ou distante da impureza. Neste caso, as evoluções temporais oscilam em torno deum valor médio não nulo e há uma larga faixa de valores de Q na qual os modos não se extinguem completamente Abstract: The description of many body systems quantum dynamics is a key ingredient for quantum computation. In the present project we study finite spin-1/2 chains dynamic properties in the presence of impurities or defects. We adopt the quantum Ising model with transverse field, of which it is possible to obtain the energy spectrum by exact calculations in the presence of one impurity. The system dynamics is driven exclusively by quantum fluctuations, whose origin is the Uncertainty Principle. We investigate the relaxation of initial states characterized by spatially inhomogeneous magnetization without any hypothesis about the proximity with the equilibrium state. Thus, the initial density matrix will be dependent of only one spatial coordinate. The investigation then is realized through the temporal evolution of the magnetization's Fourier components. Exact solutions, analytical and numerical, are obtained. One of the goals of this work consist in the search of slow relaxation processes. For the analytical cases (periodic and anti-periodic impurities) we observe oscillatory relaxations with a decay given by a power law in time (t/tQ)-vQ, where tQ and vQ are two free parameters and Q is the wave number associated to a Fourier component. There is a criticality in the exponent vQ: its value changes from 3/2 to 1/2 for certain critical values of Q. On the other hand, for the numerical cases (arbitrary impurities), the relaxation processes are distinct from the cases cited above. The initial state analyzed is a ferromagnetic direct product with only one flipped spin, near or far from the impurity. In this case, the temporal evolutions oscillate around a finite mean value and there is a large interval of Q values in which the modes do not extinguish completely Mestrado Física da Matéria Condensada Mestra em Física

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Schossler, Matheus de Oliveira. "Dinâmica de operadores de dois spins no modelo XX." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/76/76131/tde-15092017-090718/.

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Propriedades dinâmicas de sistemas quânticos de muitos corpos é um tópico de grande interesse em física da matéria condensada. Estas propriedades nos dão informação sobre a propagação de excitações elementares e de mecanismos de relaxação em sistemas interagentes. Neste contexto, as funções de correlação tem se tornado ainda mais relevantes devido a experimentos em sistemas de átomos frios e íons armadilhados que medem diretamente no domínio temporal os comportamentos assintóticos no tempo. No entanto, até o momento a maioria dos estudos em cadeias de spin quânticas focaram-se em correlações de um único spin. Utilizando a cadeia de spin XX unidimensional, nós estudamos métodos exatos para calcular as funções de correlação das componentes do tensor de dois spins, Tabi,j = SaiSbj. Estes operadores aparecem, por exemplo, como a resposta da seção de choque de espalhamento inelástico de raios X. Baseados no teorema de Wick, nós mostramos que algumas funções de correlação das componentes locais do tensor de dois operadores de spins de sítios vizinhos, na representação de férmions, podem ser escritas como uma combinação de funções de Green de uma única partícula. Utilizamos diagramas de Feynman para organizar esta combinação e calcular as funções de correlação. Em seguida, considerando esses propagadores para tempos longos e grandes distâncias ao longo do cone de luz, encontramos o comportamento dessas funções de correlação como leis de potência oscilatórias que decaem com o tempo e distância. Uma aplicação direta das funções de correlação é para o estudo de quantidades conservadas e não conservadas, uma análise sobre algumas dessas quantidades foi feita. Discutimos também as funções de correlação das componentes do tensor que não são locais na representação fermiônica. Nesse caso os cálculos foram mais desafiadores, mas usamos o fato que funções de correlação dependente do tempo podem ser expressadas em termos dos determinantes de Fredholm. Dynamical properties of quantum many body systems is a major topic of interest in condensed matter physics. These properties tell us about the propagation of elementary excitation and mechanisms of relaxation in interacting systems. In this context correlation functions have became even more relevant due the experiments in systems of cold atoms and trapped ions that measure real time dependence directly out to relatively long times. However, most studies in quantum spins chains so far have focused on correlations of single spins. Using the one dimensional XX spin chain, we study exact methods to calculate the correlation functions of the components of the tensor operator involving two spins, Tabi,j = SaiSbj. This operator appear, for example, as a response of inelastic x-ray scattering cross section. Based on Wick\'s theorem, we show that some correlation functions of local components of the tensor operator of two pairs of neighbor sites, in the fermion space, can be written as a combination of Greens functions of a single particle. We have used Feynman diagrams to organize this combination and calculate the correlation functions. Then, considering these propagators for long times and large distances along the light cone, we found the behavior of these correlation functions as a oscillatory and power law decay on time. A direct application of correlation functions is to study conserved and non-conserved quantities, and such analysis has been made. We also considered other two-spin operators which are not local in the fermionic representation. In this case the calculation is more challenging, but the time-dependent correlation functions can be expressed in terms of Fredholm determinants.

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Halász, Gábor B. "Doping a topological quantum spin liquid : slow holes in the Kitaev honeycomb model." Thesis, University of Oxford, 2015. https://ora.ox.ac.uk/objects/uuid:928ba58d-c69c-4e85-8d49-677d7e9c0fdc.

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We present a controlled microscopic study of hole dynamics in both a gapped and a gapless quantum spin liquid. Our approach is complementary to previous phenomenological works on lightly doped quantum spin liquids as we introduce mobile holes into the ground state of the exactly solvable Kitaev honeycomb model. In the spatially anisotropic (Abelian) gapped phase of the model, we address the properties of a single hole [its internal degrees of freedom as well as its hopping properties], a pair of holes [their absolute and relative particle statistics as well as their interactions], and the collective state for a finite density of holes. Our main result is that the holes in the doped model possess internal degrees of freedom as they can bind the fractional excitations of the undoped model and that the resulting composite holes with different excitations bound are distinct fractional particles with fundamentally different single-particle properties and different experimental signatures in the multi-particle ground state at finite doping. For example, some hole types are free to hop in two dimensions, while others are confined to hop in one dimension only. Also, distinct hole types have different particle statistics and, in particular, some of them exhibit non-trivial (anyonic) relative statistics. At finite doping, the respective hopping dimensionalities manifest themselves in an electrical conductivity that is either approximately isotropic or extremely anisotropic. In the gapless phase of the model, we consider a single hole and address the possibility of a coherent quasiparticle description. Our main result is that a mobile hole has a finite quasiparticle weight which vanishes in the stationary limit. Although this result is obtained in terms of an approximate variational state, we argue that it is also applicable for the exact ground state of the doped model.

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Medeiros, Marcos Henrique Lima de. "Propagação de excitações de carga e spin em isolantes topológicos 2D." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-11102017-132437/.

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Neste trabalho, nossa principal motivação foi o entendimento da dinâmica de pacotes de onda em isolantes topológicos 2D. Como excitações de carga se movem nesses materiais? De que maneira essas trajetórias dependem das condições iniciais, e de que forma as condições de contorno influenciam nessa dinâmica? Essas foram algumas das perguntas que guiaram nosso trabalho. Através de simulações computacionais, estudamos o movimento de pacotes de onda gaussianos em poços quânticos de HgTe/CdTe. O comportamento de isolante topológico para essa heteroestrutura foi prevista teoricamente no importante trabalho de Bernevig et al. (Science, vol. 314, no. 5806, 2006) e confirmada experimentalmente por König et al. (Science, vol. 318, no. 5851, 2007). Estudando-se a evolução temporal desse sistema, foi possível observar trajetórias que dependem de forma evidente, não apenas da orientação de spin, mas também da orientação de um pseudo-spin proveniente do modelo BHZ. Em sistemas com condições de contorno periódicas em ambas as dimensões e sem a aplicação de campos externos, foram observadas trajetórias com formato de espiral, acompanhadas por um \"side-jump\" dependente da direção do spin e do pseudo-spin. Em especial, para o caso em que o pseudo-spin está inicialmente orientado na direção-z, as trajetórias espiraladas foram subtituidas por um padrão do tipo \"zitterbewegung\" dependente de um potencial de \"bias\". Para sistemas confinados com bordas impenetráveis, observou-se a formação de estados de borda helicais característicos de isolantes topológicos. In this work, our main motivation was the understanding about the dynamics of wave packets in 2D topological insulators. How charge excitations move throughout theses materials? In what way their trajectories depend on the initial conditions, and how boundary conditions change this dynamics? These were some of the questions that have guided us in our work. Using numerical simulations, we have studied the movement of gaussian wave packets in HgTe/CdTe quantum wells. The topological insulator behavior for this heterostructure was theoretically predicted on the important work conducted in 2006 by Bernevig et al. (Science, vol. 314, n. 5806, 2006), and experimentally confirmed by König et al. (Science, vol. 318, no. 5851, 2007) a year later. Studing the time evolution of this system, was possible to observe trajectories that depend evidently, not only from the spin projection, but also from the pseudospin orientation coming from the BHZ model. From simulations with periodic boundary conditions in both of the two dimensions, and without the application of any external fields, we observed spiral trajectories accompanied by a spin and pseudospin dependent side-jump. Especially, for the case in which the pseudospin was iniatially oriented in \"z\" direction, the spiral trajectories were replaced by a pattern of the type \"zitterbewegung\" dependent of a bias potential. For the confined systems with barriers of hardwall type, was observed the formation of helical edge states, that is the fingerprint of topological insulators.

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Collet, François. "Short scale study of 4-simplex assembly with curvature, in euclidean Loop Quantum Gravity." Thesis, Aix-Marseille, 2016. http://www.theses.fr/2016AIXM4076/document.

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Une étude d'un assemblage symétrique de trois 4-simplex en géométrie classique, de Regge et quantique. Nous étudions les propriétés géométriques et surtout la présence de courbure. Nous montrons que les géométries classique et de Regge de l'assemblage ont une courbure qui évolue en fonction de ses paramètres de bordure. Pour la géométrie quantique, une version euclidienne du modèle EPRL est utilisé avec une valeur pratique du paramètre Barbero-Immirzi pour définir l'amplitude de transition de l'ensemble et de ses composants. Un code C ++ est conçu pour calculer les amplitudes et étudier numériquement la géométrie quantique. Nous montrons qu'une géométrie classique, avec une courbure, émerge déjà à bas spin. Nous reconnaissons également l'apparition de configurations dégénérées et de leurs effets sur la géométrie attendue A study of symmetrical assembly of three euclidean 4-simplices in classical, Regge and quantum geometry. We study the geometric properties and especially the presence of curvature. We show that classical and Regge geometry of the assembly have curvature which evolves in function of its boundary parameters. For the quantum geometry, a euclidean version of EPRL model is used with a convenient value of the Barbero-Immirzi parameter to define the transition amplitude of the assembly and its components. A C++ code is design for compute the amplitudes and study numerically the quantum geometry. We show that a classical geometry, with curvature, emerges already at low spin. We also recognize the appearance of the degenerate configurations and their effects on the expected geometry

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Chagas, Emiliano Augusto. "Quebra de simetria e transição de fase quântica em alguns modelos de acoplamento spin-boson." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/278181.

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Orientador: Kyoko Furuya Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin Made available in DSpace on 2018-08-10T14:44:05Z (GMT). No. of bitstreams: 1 Chagas_EmilianoAugusto_M.pdf: 5122954 bytes, checksum: a280b293a78cd819e62e73692ae4b99f (MD5) Previous issue date: 2008 Resumo: Neste trabalho estudamos o efeito sobre a Transição de Fase Quântica (TFQ) do Modelo de Dicke Integrável devido a adição de um pequeno termo (fixo) de interação de dois bósons na Aproximação de Onda Girante (RWA). Mostramos que, embora a descontinuidade na derivada da energia do Estado Fundamental (EF) como função do parâmetro principal de interação ('lambda') continue presente para qualquer valor de spin (J), o emaranhamento entre spin e boson sofre uma mudança bastante significativa devido à perturbação, especialmente no limite de grandes valores de J (N = 2J >> 1). Este comportamento novo é entendido através do estudo conjunto de duas quantidades como função de 'lambda' (interação) e J (tamanho do spin), a saber: (i) o ponto fixo e vizinhanças da dinâmica no espaço de fase de spin do análogo clássico do modelo e (ii) a Função de Wigner de spin EF do sistema nas vizinhanças do máximo Abstract: In this work we study the effect on the Quantum Phase Transition (QPT) of the integrable version of the Dicke model when we add a small (fixed) two boson interaction in the Rotating Wave Approximation (RWA). We show that, although the discontinuity of the Ground State (GS) energy derivative as a function of the principal parameter of interaction ('lambda') remains present for any value of spin (J), the entanglement between the spin and boson undergoes a significant change due the perturbation, specially in the limit of large values of J (N = 2J >> 1). This new behavior has been understood through the combined study of two quantities as a function of 'lambda' (interaction) and J (size of the spin): (i) the fixed point and its vicinity in the dynamics of the spin phase space o the model¿s classical analogue, and (ii) the behavior of the maxima of the spin Wigner function and its vicinity for the GS of the system Mestrado Física Mestre em Física

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Fuchs, Moritz Jakob [Verfasser], Björn [Gutachter] Trauzettel, and Haye [Gutachter] Hinrichsen. "Spin dynamics in the central spin model: Application to graphene quantum dots / Moritz Jakob Fuchs. Gutachter: Björn Trauzettel ; Haye Hinrichsen." Würzburg : Universität Würzburg, 2016. http://d-nb.info/1112041400/34.

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Goldstein, Garry. "Applications of Many Body Dynamics of Solid State Systems to Quantum Metrology and Computation." Thesis, Harvard University, 2012. http://dissertations.umi.com/gsas.harvard:10555.

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This thesis describes aspects of dynamics of solid state systems which are relevant to quantum metrology and computation. It may be divided into three research directions (parts). For the first part, a new method to enhance precision measurements that makes use of a sensor’s environment to amplify its response to weak external perturbations is described. In this method a “central” spin is used to sense the dynamics of surrounding spins, which are affected by the external perturbations that are being measured. The enhancement in precision is determined by the number of spins that are coupled strongly to the central spin and is resilient to various forms of decoherence. For polarized environments, nearly Heisenberg-limited precision measurements can be achieved. The second part of the thesis focuses on the decoherence of Majorana fermions. Specializing to the experimentally relevant case where each mode interacts with its own bath we present a method to study the effect of external perturbations on these modes. We analyze a generic gapped fermionic environment (bath) interacting via tunneling with individual Majorana modes - components of a qubit. We present examples with both static and dynamic perturbations (noise), and derive a rate of information loss for Majorana memories, that depends on the spectral density of both the noise and the fermionic bath. For the third part of the thesis we discuss vortices in topological superconductors which we model as closed finite systems, each with an odd number of real fermionic modes. We show that even in the presence of many-body interactions, there are always at least two fermionic operators that commute with the Hamiltonian. There is a zero mode corresponding to the total Majorana operator [1] as well as additional linearly independent zero modes, one of which is continuously connected to the Majorana mode in the non-interacting limit. We also show that in the situation where there are two or more well separated vortices their zero modes have non-Abelian Ising statistics under braiding. Physics

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Shinjo, Kazuya. "Density-matrix renormalization group study of quantum spin systems with Kitaev-type anisotropic interaction." 京都大学 (Kyoto University), 2016. http://hdl.handle.net/2433/215292.

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46

Skinner, Andrew J. "Hydrogenic spin quantum computing in silicon and damping and diffusion in a chain-boson model." College Park, Md. : University of Maryland, 2006. http://hdl.handle.net/1903/3887.

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Thesis (Ph. D.)--University of Maryland, College Park, 2006. Thesis research directed by: Physics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

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Penteado, Poliana Heiffig. "Transport through leaked Majorana modes in quantum dots and adatoms." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/76/76131/tde-13012014-135024/.

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We investigate quantum resonant transport in two different systems: (i) a ferromagnetic Scanning Tunneling Microscope (STM) tip coupled to an adatom (interacting) on a host surface (metallic or semiconductor), and (ii) a quantum dot connected to source and drain leads and side-coupled to a superconducting nanowire sustaining Majorana zero modes (Kitaev chain). Both problems are studied within the Green’s functions approach, which allows us to determine the transport properties of the system. In the first setup, due to the ferromagnetic and nonmagnetic ‘natures’ of the tip and host, respectively, it is possible to obtain the spin-diode effect, which occurs only in the singly occupied regime. In addition, because of the presence of the adsorbed atom on the surface, Friedel oscillations are observed in the current. The second system differs from the first mainly because it is spinless and there is no Coloumb interaction. Interestingly, we find that the Majorana mode of the wire leaks into the dot thus giving rise to a Majorana (zero mode) resonance in the dot, pinned to the Fermi level of the leads. Surprisingly, this resonance occurs even when the gate-controlled dot level is far above or far below the Fermi level of the leads. We study three possible experimental scenarios to probe unambigoulsy this Majorana mode in wires via these leaked/pinned modes. Nesta tese investigamos transporte quântico ressonante em dois sistemas diferentes: (i) uma ponta STM ferromagnética acoplada a um átomo (interagente) adsorvido em uma superfície metálica ou semicondutora, e (ii) um ponto quântico conectado a reservatórios de elétrons e lateralmente acoplado a um nanofio supercondutor que possui modos de Majorana (cadeia Kitaev). Ambos os problemas são estudados no contexto de funções de Green, o que nos permite determinar as propriedades de transporte do sistema. Na primeira configuração, devido à natureza ferromagnética e não magnética da ponta STM e da superfície e, respectivamente, é possível obter o efeito diodo de spin, que ocorre apenas no regime em que o adátomo está ocupado com um único elétron. Além disso, por causa da presença do átomo adsorvido sobre a superfície, oscilções de Friedel são observadas na corrente. O segundo sistema é diferente do primeiro, principalmente pela ausência da interação de Coloumb e pelo fato de não ter spin. Curiosamente, vemos que o modo de Majorana do fio vai para o ponto quântico dando origem assim a um modo com energia zero no ponto quântico localizado sempre no nível de Fermi dos contatos. Surpreendentemente, essa ressonância ocorre mesmo quando o nível do ponto quântico, controlado por uma tensão externa, está muito acima ou muito abaixo do nível de Fermi dos contatos. Propomos três possíveis cenários experimentais para identificar de maneira conclusiva este modo de Majorana em fios através do modo que aparece no ponto quântico.

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Santos, Marcelo Meireles dos. "A evolução temporal de sistemas de spins 1/2 congelados no espaço e descritos pelo modelo de Heisenberg." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-27032013-120632/.

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Este projeto se destina ao estudo de sistemas quânticos não relativísticos de dois, quatro e oito níveis de energia que descrevem partículas com spin s=1/2 sujeitas à ação de campos externos e interagentes entre si. São apresentadas soluções exatas para as equações que regem esses sistemas. Tais sistemas possuem uma vasta aplicação em diversas áreas da física, dentre as quais é possível destacar a computação quântica. Possíveis aplicações dos resultados são a construção de portas lógicas quânticas universais. Estas portas lógicas quânticas representam um elemento essencial no desenvolvimento dos chamados computadores quânticos. A análise e a implementação destes computadores quânticos exige a manipulação de sistemas de vários níveis, sujeitos a campos externos dependentes do tempo. Neste trabalho é apresentada a solução para o assim chamado Problema de Rabi, um particular problema de dois níveis. Um exemplo de solução para o sistema de quatro níveis, aqui relativo a um problema de dois spins também é discutido. Foram obtidas soluções exatas para sistemas de oito níveis cuja possível aplicação é a Correção Quântica de Erros. This project aims to study the non-relativistic quantum systems of two, four and eight energy levels that describe particles with spin s=1/2 in external .elds and interacting with each other. We find exact analitical solutions for these systems. Such systems have extensive applications in various areas of physics, among which its possible to highlight quantum computing. Possible applications of the results are the construction of quantum universal logic gates.These quantum logic gates are an essential element in the development of so-called quantum computers. The analysis and implementation of quantum computers requires handling systems of various levels, subject to time-dependent external fields. This work presents a solution to the so-called Rabi problem, a particular problem at two levels. An example of a solution to the system of four levels, related to two spins problem is also investigated. We obtained exact solutions for systems of eight levels with possible application to the Quantum Error Correction.

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Deng, Kuangyin. "Exchange and superexchange interactions in quantum dot systems." Diss., Virginia Tech, 2021. http://hdl.handle.net/10919/102342.

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Semiconductor quantum dot systems offer a promising platform for quantum computation. And these quantum computation candidates are normally based on spin or charge properties of electrons. In these systems, we focus on quantum computation based on electron spins since these systems has good scalability, long coherence times, and rapid gate operations. And this thesis focuses on building a theoretical description of quantum dot systems and the link between theory and experiments. In many quantum dot systems, exchange interactions are the primary mechanism used to control spins and generate entanglement. And exchange energies are normally positive, which limits control flexibility. However, recent experiments show that negative exchange interactions can arise in a linear three-dot system when a two-electron double quantum dot is exchange coupled to a larger quantum dot containing on the order of one hundred electrons. The origin of this negative exchange can be traced to the larger quantum dot exhibiting a spin triplet-like rather than singlet-like ground state. Here we show using a microscopic model based on the configuration interaction (CI) method that both triplet-like and singlet-like ground states are realized depending on the number of electrons. In the case of only four electrons, a full CI calculation reveals that triplet-like ground states occur for sufficiently large dots. These results hold for symmetric and asymmetric quantum dots in both Si and GaAs, showing that negative exchange interactions are robust in few-electron double quantum dots and do not require large numbers of electrons. Recent experiments also show the potential to utilize large quantum dots to mediate superexchange interaction and generate entanglement between distant spins. This opens up a possible mechanism for selectively coupling pairs of remote spins in a larger network of quantum dots. Taking advantage of this opportunity requires a deeper understanding of how to control superexchange interactions in these systems. Here, we consider a triple-dot system arranged in linear and triangular geometries. We use CI calculations to investigate the interplay of superexchange and nearest-neighbor exchange interactions as the location, detuning, and electron number of the mediating dot are varied. We show that superexchange processes strongly enhance and increase the range of the net spin-spin exchange as the dots approach a linear configuration. Furthermore, we show that the strength of the exchange interaction depends sensitively on the number of electrons in the mediator. Our results can be used as a guide to assist further experimental efforts towards scaling up to larger, two-dimensional quantum dot arrays. Doctor of Philosophy Semiconductor quantum dot systems offer a promising platform for quantum computation. And these quantum computation candidates are normally based on spin or charge properties of electrons. In these systems, we focus on quantum computation based on electron spins since these systems has good scalability, long coherence times, and rapid gate operations. And this thesis focuses on building a theoretical description of quantum dot systems and the link between theory and experiments. A key requirement for quantum computation is the ability to control individual qubits and couple them together to create entanglement. In quantum dot spin qubit systems, the exchange interaction is the primary mechanism used to accomplish these tasks. This thesis is about attaining a better understanding of exchange interactions in quantum dot spin qubit systems and how they can be manipulated by changing the configuration of the system and the number of electrons. In this thesis, we show negative exchange energy can arise in large size quantum dots. This result holds for symmetric and asymmetric shape of the large dots. And we also provide a quantitative analysis of how large quantum dots can be used to create long-distance spin-spin interactions. This capability would greatly increase the flexibility in designing quantum processors built by quantum dot spins. The interplay of these systems with different geometry can serve as a guide to assist further experiments and may hopefully be the basis to build two-dimensional quantum dot arrays.

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Grijalva, Sebastian. "Boundary effects in quantum spin chains and Finite Size Effects in the Toroidal Correlated Percolation model." Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASP093.

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Cette thèse est divisée en deux parties : la première présente un modèle statistique en deux dimensions de percolation corrélée sur un réseau toroïdal. Nous présentons un protocole pour construire des surfaces corrélées à longue portée sur la base de surfaces gaussiennes fractionnaires, puis nous relions les ensembles de niveaux à une famille de modèles de percolation corrélés. Les clusters émergents sont ensuite étudiés numériquement, et nous testons leur symétrie conforme en vérifiant que les corrections de taille finie de connectivité à deux points suivent les prédictions de la théorie des champs conformes. Nous commentons également le comportement des fonctions à trois points et fournissons un code numérique pour reproduire les résultats. La deuxième partie de la thèse étudie la chaîne quantique XXZ intégrable de spin-1/2 avec des conditions aux bords ouvertes, pour un nombre pair et impair de sites. Dans régime antiferromagnétique, nous utilisons l'Ansatz de Bethe Algébrique pour déterminer les configurations possibles en termes des champs aux bords. On retrouve les conditions d'existence d'états fondamentaux quasi dégénérés séparés par un gap au reste du spectre. Nous calculons l'aimantation au bord à température nulle et constatons qu'elle dépend du champ sur le bord opposé même dans la limite de chaîne semi-infinie. Nous calculons enfin la fonction d'autocorrélation temporelle au bord et montrons que dans le cas de taille paire, elle est finie à la limite de temps long à cause de la quasi-dégénérescence This thesis is divided in two parts: The first one presents a 2D statistical model of correlated percolation on a toroidal lattice. We present a protocol to construct long-range correlated surfaces based on fractional Gaussian surfaces and then we relate the level sets to a family of correlated percolation models. The emerging clusters are then numerically studied, and we test their conformal symmetry by verifying that their planar-limit finite-size corrections follow the predictions of Conformal Field Theory. We comment also the behavior of three-point functions and provide a numerical code to reproduce the results.The second part of the thesis studies the quantum integrable XXZ spin-1/2 chain with open boundary conditions for even and odd number of sites. We concentrate in the anti-ferromagnetic regime and use the Algebraic Bethe Ansatz to determine the configurations that arise in terms of the boundary fields. We find the conditions of existence of quasi-degenerate ground states separated by a gap to the rest of the spectrum. We calculate the boundary magnetization at zero temperature and find that it depends on the field at the opposite edge even in the semi-infinite chain limit. We finally calculate the time autocorrelation function at the boundary and show that in the even-size case it is finite for the long-time limit as a result of the quasi-degeneracy

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