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Relevant bibliographies by topics / Density Matrix Renormalization Group (DMRG) algorithm

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Academic literature on the topic 'Density Matrix Renormalization Group (DMRG) algorithm'

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Published: 22 February 2023

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Journal articles on the topic "Density Matrix Renormalization Group (DMRG) algorithm"

1

Schollwöck, Ulrich. "The density-matrix renormalization group: a short introduction." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1946 (July 13, 2011): 2643–61. http://dx.doi.org/10.1098/rsta.2010.0382.

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The density-matrix renormalization group (DMRG) method has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. The DMRG is a method that shares features of a renormalization group procedure (which here generates a flow in the space of reduced density operators) and of a variational method that operates on a highly interesting class of quantum states, so-called matrix product states (MPSs). The DMRG method is presented here entirely in the MPS language. While the DMRG generally fails in larger two-dimensional systems, the MPS picture suggests a straightforward generalization to higher dimensions in the framework of tensor network states. The resulting algorithms, however, suffer from difficulties absent in one dimension, apart from a much more unfavourable efficiency, such that their ultimate success remains far from clear at the moment.

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SCHOLLWÖCK, ULRICH. "RECENT PROGRESS IN THE DENSITY-MATRIX RENORMALIZATION GROUP." International Journal of Modern Physics B 21, no. 13n14 (May 30, 2007): 2564–75. http://dx.doi.org/10.1142/s0217979207043890.

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Over the last decade, the density-matrix renormalization group (DMRG) has emerged as the most powerful method for the simulation of strongly correlated one-dimensional (1D) quantum systems. Input from quantum information has allowed to trace the method's performance to the entanglement properties of quantum states, revealing why it works so well in 1D and not so well in 2D; it has allowed to devise algorithms for time-dependent quantum systems and, by clarifying the link between DMRG and Wilson's numerical renormalization group (NRG), for quantum impurity systems.

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Devakul, Trithep, Vedika Khemani, Frank Pollmann, David A. Huse, and S. L. Sondhi. "Obtaining highly excited eigenstates of the localized XX chain via DMRG-X." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 375, no. 2108 (October 30, 2017): 20160431. http://dx.doi.org/10.1098/rsta.2016.0431.

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We benchmark a variant of the recently introduced density matrix renormalization group (DMRG)-X algorithm against exact results for the localized random field XX chain. We find that the eigenstates obtained via DMRG-X exhibit a highly accurate l-bit description for system sizes much bigger than the direct, many-body, exact diagonalization in the spin variables is able to access. We take advantage of the underlying free fermion description of the XX model to accurately test the strengths and limitations of this algorithm for large system sizes. We discuss the theoretical constraints on the performance of the algorithm from the entanglement properties of the eigenstates, and its actual performance at different values of disorder. A small but significant improvement to the algorithm is also presented, which helps significantly with convergence. We find that, at high entanglement, DMRG-X shows a bias towards eigenstates with low entanglement, but can be improved with increased bond dimension. This result suggests that one must be careful when applying the algorithm for interacting many-body localized spin models near a transition. This article is part of the themed issue ‘Breakdown of ergodicity in quantum systems: from solids to synthetic matter’.

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MARTÍN-DELGADO, MIGUEL A., and GERMÁN SIERRA. "ANALYTIC FORMULATIONS OF THE DENSITY MATRIX RENORMALIZATION GROUP." International Journal of Modern Physics A 11, no. 17 (July 10, 1996): 3145–74. http://dx.doi.org/10.1142/s0217751x96001516.

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We present two new analytic formulations of the density matrix renormalization group (DMRG) method. In these formulations we combine the block renormalization group (BRG) procedure with the variational and Fokker-Planck methods. The BRG method is used to reduce the lattice size while the latter are used to construct approximate target states to compute the block density matrix. We apply our DMRG methods to the Ising model in a transverse field (ITF model) and compute several of its critical properties, which are then compared with the old BRG results.

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MA, HAIBO, CHUNGEN LIU, and YUANSHENG JIANG. "BLOCK DENSITY MATRIX RENORMALIZATION GROUP WITH EFFECTIVE INTERACTIONS." Journal of Theoretical and Computational Chemistry 08, no. 05 (October 2009): 837–48. http://dx.doi.org/10.1142/s0219633609005064.

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Based on the contractor renormalization group (CORE) method and the density matrix renormalization group (DMRG) method, a new computational scheme, which is called the block density matrix renormalization group with effective interactions (BDMRG-EI), is proposed to deal with the numerical computation of quantum correlated systems. Different from the conventional CORE method in calculating the blocks and the fragments, where the DMRG method instead of the exact diagonalization is employed in BDMRG-EI, BDMRG-EI makes the calculations of larger blocks and fragments applicable. Integrating DMRG's advantage of high accuracy and CORE's advantage of low computational costs, BDMRG-EI can be widely used for the theoretical calculations of the ground state and low-lying excited states of large systems with simple or complicated connectivity. Test calculations on a 240 site one-dimensional chain and a double-layer polyacene oligomer containing 48 hexagons with the spin-1/2 Heisenberg Hamiltonian demonstrate the efficiency and potentiality of the method.

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Sharma, Prachi, Varinia Bernales, Stefan Knecht, Donald G. Truhlar, and Laura Gagliardi. "Density matrix renormalization group pair-density functional theory (DMRG-PDFT): singlet–triplet gaps in polyacenes and polyacetylenes." Chemical Science 10, no. 6 (2019): 1716–23. http://dx.doi.org/10.1039/c8sc03569e.

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Friesecke, Gero, and Benedikt R. Graswald. "Two-electron wavefunctions are matrix product states with bond dimension three." Journal of Mathematical Physics 63, no. 9 (September 1, 2022): 091901. http://dx.doi.org/10.1063/5.0072261.

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We prove the statement in the title for a suitable (wavefunction-dependent) choice of the underlying orbitals and show that 3 is optimal. Thus, for two-electron systems, the quantum chemistry density matrix renormalization group (QC-DMRG) method with bond dimension 3 combined with fermionic mode optimization exactly recovers the full configuration-interaction (FCI) energy.

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Akutsu, Noriko. "Density-matrix renormalization-group study for a two-dimensional lattice-gas on the Ih-ice prism surface." Journal of Physics: Conference Series 2207, no. 1 (March 1, 2022): 012036. http://dx.doi.org/10.1088/1742-6596/2207/1/012036.

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Abstract The phase transition temperature of a two-dimensional (2D) lattice-gas model for the Ih-ice prism surface ((1010) surface on a wurtzite crystal structure) is calculated using the density-matrix renormalization-group (DMRG) method. Since the unit cell on the prism surface contains four atoms without inversion symmetry, the asymmetric version of the DMRG is required to obtain a precise value of the phase transition temperature. The effective bond energy on the surface is obtained by comparing the phase transition temperature with the faceting transition temperature observed for a real ice crystal. Using the effective bond energy, the temperature dependence of the coverage on sub-lattice sites is calculated. The surface tensions on the (0001) surface (the basal plane) and the prism plane are also calculated. The surface tension of the basal plane for the ice/water interface agrees well with the recent calculated values obtained by large scale molecular dynamics.

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LI, SHUHUA, JING MA, and YUANSHENG JIANG. "HEISENBERG MODEL AND ITS APPLICATIONS TO π-CONJUGATED SYSTEMS." Journal of Theoretical and Computational Chemistry 01, no. 02 (October 2002): 351–71. http://dx.doi.org/10.1142/s0219633602000270.

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This paper briefly reviewed the Heisenberg model and its improvement by including higher order corrections, and their applications to bond lengths, stability, and reactivity of non-benzenoids and the low-lying excitation spectra of conjugated systems. Two efficient computational methods, the Lanczos method and the density-matrix renormalization group (DMRG), for exactly and approximately solving various Heisenberg models, respectively, were briefly introduced.

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McCulloch, I. P., and M. Gulácsi. "The non-Abelian density matrix renormalization group algorithm." Europhysics Letters (EPL) 57, no. 6 (March 2002): 852–58. http://dx.doi.org/10.1209/epl/i2002-00393-0.

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Dissertations / Theses on the topic "Density Matrix Renormalization Group (DMRG) algorithm"

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Rossini, Davide. "Quantum information processing and Quantum spin systems." Doctoral thesis, Scuola Normale Superiore, 2007. http://hdl.handle.net/11384/85856.

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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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Hager, Georg. "A parallelized density matrix renormalization group algorithm and its application to strongly correlated systems." [S.l.] : [s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=984380590.

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Paulino, Neto Romain. "Développement et application de méthodes corrélées pour la description de systèmes moléculaires." Thesis, Paris 6, 2014. http://www.theses.fr/2014PA066216/document.

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Ces travaux de thèse se sont concentrés sur le développement, l'implémentation et l'application de différents types de méthodes quantiques prenant la corrélation électronique en compte, dans le but de fournir des outils performants pour la description de systèmes moléculaires à l'état fondamental et excité. La méthode dite DMRG (Density Matrix Renormalization Group) a été étudiée et un logiciel correspondant a été développé en FORTRAN. Cette méthode permet de limiter le nombre d'états électroniques à prendre en compte, ce qui fait gagner du temps de calcul, tout en assurant une précision des résultats du même ordre que celle fournie par les toutes meilleures méthodes post-Hartree-Fock actuelles. Dans la deuxième partie de cette thèse, nous avons utilisé une autre méthode : la DFT (Density Functional Theory). Une étude théorique a été effectuée sur deux fonctionnelles à séparation de portée (HISS-A et -B) afin d'évaluer dans quelle mesure ces fonctionnelles, développées au départ pour l'étude des systèmes métalliques, pouvaient être appliquées à la description de l'état fondamental et excité de systèmes moléculaires hautement conjugués. Nous avons également utilisé la DFT afin de modéliser et rationaliser le comportement photo-physique d'un composé moléculaire présentant une émission dite " duale ". Nous avons pu ainsi caractériser le comportement complexe de la molécule à l'état excité et expliquer les résultats surprenants qui avaient été observés, en particulier au niveau des spectres d'émission UV et d'excitation de fluorescence. Le phénomène d'émission duale observé a ainsi pu être lié à la présence d'un degré de liberté conformationnel important de la molécule
In the last few years, a lot of energy has been put forward in the area of quantum chemistry to develop new methods, or to improve existing methods, that are able to describe very precisely the electronic structure of molecular systems. In this manuscript, a precise overview of such a method (namely the Density Matrix Renormalization Group, DMRG method) is given. A software able to carry out DMRG calculations has indeed been developed from scratch in the laboratory during this thesis. This method can be seen as a post-Hartree-Fock method, in which only the electronic states that are relevant for the correct description of the molecule are kept. In this way, the computational cost remains acceptable, and the results are in line with those given by "exact" methods such as full-CI. Density Functional Theory (DFT) has also been investigated in this work. DFT and TD-DFT calculations have indeed also been carried out. The performances of two middle-range-separated functionals, namely HISS-A and HISS-B, to describe electronic transitions in conjugated molecules have been probed in a theory vs. theory study. Those functionals, which had been first developed for the study of metals, show to be adequate for the correct description of electronic excitations of chromophores and of push-pull molecules. Optical properties of a dual emittor have also been studied using TD-DFT. The dual emission of this molecule has been shown to stem from the presence of two distinct emissive states, respectively of Intramolecular Charge Transfer (ICT) and locally excited (LE) nature. TD-DFT has allowed us to link those two emissive states to two different conformations of the molecule

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Peotta, Sebastiano. "Nonequilibrium dynamics of strongly correlated one-dimensional ultracold quantum gases." Doctoral thesis, Scuola Normale Superiore, 2013. http://hdl.handle.net/11384/85863.

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In the original work of this Thesis we use Time Dependent Density Matrix Renormalization Group (TDMRG) to follow and study the unitary dynamics of 1D strongly interacting quantum systems. In the rest part we present our work on the collision of spin polarized fermionic clouds. We study spin drag e ects immediately after the collision. This work is relevant to current experiments where pure spin currents have been realized with ultracold atomic gases. Several of our predictions can be veri ed in future experiments on strongly interacting few-fermion systems. In the second part the highly imbalanced case of an impurity immersed in a bath of bosonic atoms is considered. The interaction of the impurity with the bath manifests in the mass renormalization and in the damping of the oscillations of the breathing mode of the impurity in a harmonic potential. We compare the TDMRG results with an analytically tractable model in which the bath is treated as a Luttinger liquid and pinpoint striking deviations from this picture due to the nonlinear nature of the Lieb-Liniger gas. This results are relevant to current and future experiments on impurities coupled to one-dimensional ultracold gases. Finally, we employ DMRG to study spin-orbit coupled bosons in 1D optical lattices, following recent remarkable experimental advances on arti cially engineered gauge elds and spin-orbit coupling in ultracold atoms. We concentrate in the Mott insulator region of the phase diagram of pseudospin-1/2 bosons with spin-orbit coupling and anisotropic interaction terms that fully break spin rotational symmetry.

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Baiardi, Alberto. "Development of computational methods for the simulation of vibrational and electronic spectra of medium-to-large sized molecular systems." Doctoral thesis, Scuola Normale Superiore, 2018. http://hdl.handle.net/11384/85999.

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Brandejs, Jan. "Optimalizované simulace kvantových systémů a metoda DMRG." Master's thesis, 2016. http://www.nusl.cz/ntk/nusl-351994.

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Title: Optimizing quantum simulations and the DMRG method Author: Jan Brandejs Department: Department of Chemical Physics and Optics Supervisor: doc. Dr. rer. nat. Jiří Pittner, DSc., J. Heyrovský Institute of Physical Chemistry of the Czech Academy of Sciences Abstract: In this work, we explore the quantum information theoretical aspects of simulation of quantum systems on classical computers, in particular the many- electron strongly correlated wave functions. We describe a way how to reduce the amount of data required for storing the wavefunction by a lossy compression of quantum information. For this purpose, we describe the measures of quantum entanglement for the density matrix renormalization group method. We imple- ment the computation of multi-site generalization of mutual information within the DMRG method and investigate entanglement patterns of strongly correlated chemical systems. We present several ways how to optimize the ground state calculation in the DMRG method. The theoretical conclusions are supported by numerical simulations of the diborane molecule, exhibiting chemically interest- ing electronic structure, like the 3-centered 2-electron bonds. In the theoretical part, we give a brief introduction to the principles of the DMRG method. Then we explain the quantum informational...

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Hager, Georg [Verfasser]. "A parallelized density matrix renormalization group algorithm and its application to strongly correlated systems / vorgelegt von Georg Hager." 2005. http://d-nb.info/984380590/34.

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Tiegel, Alexander Clemens. "Finite-temperature dynamics of low-dimensional quantum systems with DMRG methods." Doctoral thesis, 2016. http://hdl.handle.net/11858/00-1735-0000-0028-8801-A.

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Dutta, Tirthankar. "Real-Time DMRG Dynamics Of Spin And Charge Transport In Low-Dimensional Strongly Correlated Fermionic Systems." Thesis, 2011. http://etd.iisc.ernet.in/handle/2005/2417.

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This thesis deals with out-of-equilibrium transport phenomena in strongly correlated low-dimensional fermionic systems, with special emphasis on π-conjugated molecular materials. The focus of this work is to study real-time dynamics of spin and charge transport in these systems in order to investigate non-equilibrium transport in single-molecule electronic and spintronic devices. Chapter 1 describes the electronic structure and dynamics of strongly correlated fermionic systems in general, and in one-dimension, in particular. For this purpose, effective low-energy model Hamiltonians (used in this work) are discussed. Whenever applicable, approximate analytical and numerical methods commonly used in the literature to deal with these model Hamiltonians, are outlined. In the context of one-dimensional strongly correlated fermionic systems, analytical techniques like the Bethe ansatz and bosonization, and numerical procedures like exact diagonalization and DMRG, used for solving finite systems, are discussed in detail. Chapter 2 provides an overview of the different zero-temperature (T = 0) time-dependent DMRG algorithms, which have been used to study out-of-equilibrium time-dependent phenomena in low-dimensional strongly correlated systems. In Chapter 3 we employ the time-dependent DMRG algorithm proposed by Luo, Xiang and Wang [Phys. Rev. Lett. 91, 049701 (2003)], to study the role of dimerization and electronic correlations on the dynamics of spin-charge separation. We employ the H¨uckel and Hubbard models for our studies. We have modified the algorithm proposed by Luo et. al to overcome some of its limitations. Chapter 4 presents a generalized adaptive time-dependent density matrix renormalization group (DMRG) scheme developed by us, called the Double Time Window Targeting (DTWT) technique, which is capable of giving accurate results with lesser computational resources than required by the existing methods. This procedure originates from the amalgamation of the features of pace keeping DMRG algorithm, first proposed by Luo et. al, [Phys.Rev. Lett. 91, 049701 (2003)], and the time-step targeting (TST) algorithm by Feiguin and White [Phys. Rev. B 72, 020404 (2005)]. In chapter 5 we apply the Double Time Window Targeting (DTWT) technique, which was discussed in the previous chapter, for studying real-time quantum dynamics of spin-charge separation in π-conjugated polymers. We employ the Pariser-Parr-Pople (PPP) model which has long-range electron-electron interactions. For investigating real-time dynamics of spin and charge transport, we inject a hole at one end of polyene chains of different lengths and study the temporal evolution of its spin and charge degrees of freedom, using the DTWT td-DMRG algorithm. Chapter 6 we investigate the effect of terminal substituents on the dynamics of spin and charge transport in donor-acceptor substituted polyenes (D- (CH)x- A) chains, also known as push-pull polyenes. We employ long-range correlated model Hamiltonian for the D- (CH)x- A system and, real-time DMRG dynamics for time propagating the wave packet obtained by injecting a hole at a terminal site in the ground state of the system. Our studies reveal that the end groups do not affect the spin and charge velocities in any significant way, but change the amount of charge transported. We have compared these with the polymethineimine (CN)x system in which besides electron affinities, the nature of pz orbitals in conjugation also alternate from site to site. Chapter 7 presents our investigation on the effect of static electron-phonon coupling (dimerization) on the dynamics of spin-charge separation in particular, and transport in general, in π-conjugated polyene chains. The polyenes are modeled by the Pariser-Parr-Pople Hamiltonian, having long-range electron-electron correlations. Our studies reveal that spin and charge velocities depend both on the chain length and dimerization. The spin and charge velocities increase as dimerization increases, but the amount of charge and spin transported along the chain decrease with enhancement in dimerization. Furthermore, in the range 0.3≤ δ≤0.5, it is observed that the dynamics of spin-charge separation becomes complicated, and the charge degree of freedom is affected more by electron-phonon coupling compared to the spin degree of freedom.

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Books on the topic "Density Matrix Renormalization Group (DMRG) algorithm"

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Density Matrix Renormalization Group ( Dmrg) -Based Approaches in Computational Chemistry. Elsevier, 2022. http://dx.doi.org/10.1016/c2020-0-01314-9.

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Shuai, Zhigang, Ulrich Schollwöck, and Haibo Ma. Density Matrix Renormalization Group (DMRG)-Based Approaches in Computational Chemistry. Elsevier, 2022.

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Shuai, Zhigang, Ulrich Schollwöck, and Haibo Ma. Density Matrix Renormalization Group (DMRG)-Based Approaches in Computational Chemistry. Elsevier, 2022.

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Book chapters on the topic "Density Matrix Renormalization Group (DMRG) algorithm"

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Marti, Konrad Heinrich, and Markus Reiher. "The Density Matrix Renormalization Group Algorithm in Quantum Chemistry." In Progress in Physical Chemistry Volume 3, 293–309. München: Oldenbourg Wissenschaftsverlag GmbH, 2010. http://dx.doi.org/10.1524/9783486711639.293.

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Dolgov, Sergey V., and Dmitry V. Savostyanov. "Corrected One-Site Density Matrix Renormalization Group and Alternating Minimal Energy Algorithm." In Lecture Notes in Computational Science and Engineering, 335–43. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10705-9_33.

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Ma, Haibo, Ulrich Schollwöck, and Zhigang Shuai. "Density matrix renormalization group." In Density Matrix Renormalization Group ( Dmrg) -Based Approaches in Computational Chemistry, 1–18. Elsevier, 2022. http://dx.doi.org/10.1016/b978-0-323-85694-2.00007-3.

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Ma, Haibo, Ulrich Schollwöck, and Zhigang Shuai. "Post-density matrix renormalization group." In Density Matrix Renormalization Group ( Dmrg) -Based Approaches in Computational Chemistry, 189–246. Elsevier, 2022. http://dx.doi.org/10.1016/b978-0-323-85694-2.00009-7.

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Ma, Haibo, Ulrich Schollwöck, and Zhigang Shuai. "Time-dependent density matrix renormalization group." In Density Matrix Renormalization Group ( Dmrg) -Based Approaches in Computational Chemistry, 279–315. Elsevier, 2022. http://dx.doi.org/10.1016/b978-0-323-85694-2.00006-1.

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Ma, Haibo, Ulrich Schollwöck, and Zhigang Shuai. "Density matrix renormalization group with orbital optimization." In Density Matrix Renormalization Group ( Dmrg) -Based Approaches in Computational Chemistry, 149–88. Elsevier, 2022. http://dx.doi.org/10.1016/b978-0-323-85694-2.00008-5.

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Ma, Haibo, Ulrich Schollwöck, and Zhigang Shuai. "DMRG in frequency space." In Density Matrix Renormalization Group ( Dmrg) -Based Approaches in Computational Chemistry, 247–78. Elsevier, 2022. http://dx.doi.org/10.1016/b978-0-323-85694-2.00005-x.

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Ma, Haibo, Ulrich Schollwöck, and Zhigang Shuai. "Density matrix renormalization group for semiempirical quantum chemistry." In Density Matrix Renormalization Group ( Dmrg) -Based Approaches in Computational Chemistry, 57–90. Elsevier, 2022. http://dx.doi.org/10.1016/b978-0-323-85694-2.00002-4.

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Ma, Haibo, Ulrich Schollwöck, and Zhigang Shuai. "Density matrix renormalization group for ab initio quantum chemistry Hamiltonian." In Density Matrix Renormalization Group ( Dmrg) -Based Approaches in Computational Chemistry, 91–147. Elsevier, 2022. http://dx.doi.org/10.1016/b978-0-323-85694-2.00004-8.

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Ma, Haibo, Ulrich Schollwöck, and Zhigang Shuai. "Tensor network states: matrix product states and relatives." In Density Matrix Renormalization Group ( Dmrg) -Based Approaches in Computational Chemistry, 19–56. Elsevier, 2022. http://dx.doi.org/10.1016/b978-0-323-85694-2.00003-6.

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Conference papers on the topic "Density Matrix Renormalization Group (DMRG) algorithm"

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HIKIHARA, TOSHIYA. "DENSITY-MATRIX RENORMALIZATION GROUP METHOD FOR TOMONAGA-LUTTINGER LIQUID." In Proceedings of the Summer School on Decoherence, Entanglement & Entropy and Proceedings of the Workshop on MPS & DMRG. WORLD SCIENTIFIC, 2012. http://dx.doi.org/10.1142/9789814407199_0010.

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MATSUEDA, HIROAKI. "APPLICATION OF DENSITY MATRIX RENORMALIZATION GROUP METHOD TO PHOTOINDUCED PHENOMENA IN STRONGLY CORRELATED ELECTRON SYSTEMS." In Proceedings of the Summer School on Decoherence, Entanglement & Entropy and Proceedings of the Workshop on MPS & DMRG. WORLD SCIENTIFIC, 2012. http://dx.doi.org/10.1142/9789814407199_0009.

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Nemes, Csaba, Gergely Barcza, Zoltan Nagy, Ors Legeza, and Peter Szolgay. "Implementation trade-offs of the density matrix renormalization group algorithm on kilo-processor architectures." In 2013 European Conference on Circuit Theory and Design (ECCTD). IEEE, 2013. http://dx.doi.org/10.1109/ecctd.2013.6662251.

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