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Zeitschriftenartikel zum Thema „Lieb-Robinson bound“

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Veröffentlicht am 28. September 2024

Zuletzt aktualisiert am 31. Juli 2025

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1

Matsuta, Takuro, Tohru Koma, and Shu Nakamura. "Improving the Lieb–Robinson Bound for Long-Range Interactions." Annales Henri Poincaré 18, no. 2 (2016): 519–28. http://dx.doi.org/10.1007/s00023-016-0526-1.

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2

Woods, M. P., and M. B. Plenio. "Dynamical error bounds for continuum discretisation via Gauss quadrature rules—A Lieb-Robinson bound approach." Journal of Mathematical Physics 57, no. 2 (2016): 022105. http://dx.doi.org/10.1063/1.4940436.

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3

Mahoney, Brendan J., and Craig S. Lent. "The Value of the Early-Time Lieb-Robinson Correlation Function for Qubit Arrays." Symmetry 14, no. 11 (2022): 2253. http://dx.doi.org/10.3390/sym14112253.

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The Lieb-Robinson correlation function is one way to capture the propagation of quantum entanglement and correlations in many-body systems. We consider arrays of qubits described by the tranverse-field Ising model and examine correlations as the expanding front of entanglement first reaches a particular qubit. Rather than a new bound for the correlation function, we calculate its value, both numerically and analytically. A general analytical result is obtained that enables us to analyze very large arrays of qubits. The velocity of the entanglement front saturates to a constant value, for which

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4

Strasberg, Philipp, Kavan Modi, and Michalis Skotiniotis. "How long does it take to implement a projective measurement?" European Journal of Physics 43, no. 3 (2022): 035404. http://dx.doi.org/10.1088/1361-6404/ac5a7a.

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Abstract According to the Schrödinger equation, a closed quantum system evolves continuously in time. If it is subject to a measurement however, its state changes randomly and discontinuously, which is mathematically described by the projection postulate. But how long does it take for this discontinuous change to occur? Based on simple estimates, whose validity rests solely on the fact that all fundamental forces in nature are finite-ranged, we show that the implementation of a quantum measurement requires a minimum time. This time scales proportionally with the diameter of the quantum mechani

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5

Moosavian, Ali Hamed, Seyed Sajad Kahani, and Salman Beigi. "Limits of Short-Time Evolution of Local Hamiltonians." Quantum 6 (June 27, 2022): 744. http://dx.doi.org/10.22331/q-2022-06-27-744.

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Evolutions of local Hamiltonians in short times are expected to remain local and thus limited. In this paper, we validate this intuition by proving some limitations on short-time evolutions of local time-dependent Hamiltonians. We show that the distribution of the measurement output of short-time (at most logarithmic) evolutions of local Hamiltonians are concentrated and satisfy an isoperimetric inequality. To showcase explicit applications of our results, we study the MAXCUT problem and conclude that quantum annealing needs at least a run-time that scales logarithmically in the problem size t

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6

Vershynina, Anna, and Elliott Lieb. "Lieb-Robinson bounds." Scholarpedia 8, no. 9 (2013): 31267. http://dx.doi.org/10.4249/scholarpedia.31267.

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7

Doyon, Benjamin. "Hydrodynamic Projections and the Emergence of Linearised Euler Equations in One-Dimensional Isolated Systems." Communications in Mathematical Physics 391, no. 1 (2022): 293–356. http://dx.doi.org/10.1007/s00220-022-04310-3.

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AbstractOne of the most profound questions of mathematical physics is that of establishing from first principles the hydrodynamic equations in large, isolated, strongly interacting many-body systems. This involves understanding relaxation at long times under reversible dynamics, determining the space of emergent collective degrees of freedom (the ballistic waves), showing that projection occurs onto them, and establishing their dynamics (the hydrodynamic equations). We make progress in these directions, focussing for simplicity on one-dimensional systems. Under a model-independent definition o

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8

Islambekov, Umar, Robert Sims, and Gerald Teschl. "Lieb–Robinson Bounds for the Toda Lattice." Journal of Statistical Physics 148, no. 3 (2012): 440–79. http://dx.doi.org/10.1007/s10955-012-0554-2.

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9

NACHTERGAELE, BRUNO, BENJAMIN SCHLEIN, ROBERT SIMS, SHANNON STARR, and VALENTIN ZAGREBNOV. "ON THE EXISTENCE OF THE DYNAMICS FOR ANHARMONIC QUANTUM OSCILLATOR SYSTEMS." Reviews in Mathematical Physics 22, no. 02 (2010): 207–31. http://dx.doi.org/10.1142/s0129055x1000393x.

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We construct a W*-dynamical system describing the dynamics of a class of anharmonic quantum oscillator lattice systems in the thermodynamic limit. Our approach is based on recently proved Lieb–Robinson bounds for such systems on finite lattices [19].

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10

Nachtergaele, Bruno, and Robert Sims. "Lieb-Robinson Bounds and the Exponential Clustering Theorem." Communications in Mathematical Physics 265, no. 1 (2006): 119–30. http://dx.doi.org/10.1007/s00220-006-1556-1.

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11

Nachtergaele, Bruno, Hillel Raz, Benjamin Schlein, and Robert Sims. "Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems." Communications in Mathematical Physics 286, no. 3 (2008): 1073–98. http://dx.doi.org/10.1007/s00220-008-0630-2.

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12

Damanik, David, Marius Lemm, Milivoje Lukic, and William Yessen. "On anomalous Lieb–Robinson bounds for the Fibonacci XY chain." Journal of Spectral Theory 6, no. 3 (2016): 601–28. http://dx.doi.org/10.4171/jst/133.

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13

Sweke, Ryan, Jens Eisert, and Michael Kastner. "Lieb–Robinson bounds for open quantum systems with long-ranged interactions." Journal of Physics A: Mathematical and Theoretical 52, no. 42 (2019): 424003. http://dx.doi.org/10.1088/1751-8121/ab3f4a.

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14

Gebert, Martin, and Marius Lemm. "On Polynomial Lieb–Robinson Bounds for the XY Chain in a Decaying Random Field." Journal of Statistical Physics 164, no. 3 (2016): 667–79. http://dx.doi.org/10.1007/s10955-016-1558-0.

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15

Nachtergaele, Bruno, Robert Sims, and Amanda Young. "Quasi-locality bounds for quantum lattice systems. I. Lieb-Robinson bounds, quasi-local maps, and spectral flow automorphisms." Journal of Mathematical Physics 60, no. 6 (2019): 061101. http://dx.doi.org/10.1063/1.5095769.

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16

Bachmann, Sven, Wojciech Dybalski, and Pieter Naaijkens. "Lieb–Robinson Bounds, Arveson Spectrum and Haag–Ruelle Scattering Theory for Gapped Quantum Spin Systems." Annales Henri Poincaré 17, no. 7 (2015): 1737–91. http://dx.doi.org/10.1007/s00023-015-0440-y.

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17

Bentsen, Gregory, Yingfei Gu, and Andrew Lucas. "Fast scrambling on sparse graphs." Proceedings of the National Academy of Sciences 116, no. 14 (2019): 6689–94. http://dx.doi.org/10.1073/pnas.1811033116.

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Given a quantum many-body system with few-body interactions, how rapidly can quantum information be hidden during time evolution? The fast-scrambling conjecture is that the time to thoroughly mix information among N degrees of freedom grows at least logarithmically in N. We derive this inequality for generic quantum systems at infinite temperature, bounding the scrambling time by a finite decay time of local quantum correlations at late times. Using Lieb–Robinson bounds, generalized Sachdev–Ye–Kitaev models, and random unitary circuits, we propose that a logarithmic scrambling time can be achi

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18

Gebert, Martin, Bruno Nachtergaele, Jake Reschke, and Robert Sims. "Lieb–Robinson Bounds and Strongly Continuous Dynamics for a Class of Many-Body Fermion Systems in $${\mathbb {R}}^d$$." Annales Henri Poincaré 21, no. 11 (2020): 3609–37. http://dx.doi.org/10.1007/s00023-020-00959-5.

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19

Kennett, Malcolm P. "Out-of-Equilibrium Dynamics of the Bose-Hubbard Model." ISRN Condensed Matter Physics 2013 (June 12, 2013): 1–39. http://dx.doi.org/10.1155/2013/393616.

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The Bose-Hubbard model is the simplest model of interacting bosons on a lattice. It has recently been the focus of much attention due to the realization of this model with cold atoms in an optical lattice. The ability to tune parameters in the Hamiltonian as a function of time in cold atom systems has opened up the possibility of studying out-of-equilibrium dynamics, including crossing the quantum critical region of the model in a controlled way. In this paper, I give a brief introduction to the Bose Hubbard model, and its experimental realization and then give an account of theoretical and ex

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20

Hinrichs, Benjamin, Marius Lemm, and Oliver Siebert. "On Lieb–Robinson Bounds for a Class of Continuum Fermions." Annales Henri Poincaré, July 12, 2024. http://dx.doi.org/10.1007/s00023-024-01453-y.

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AbstractWe consider the quantum dynamics of a many-fermion system in $${{\mathbb {R}}}^d$$ R d with an ultraviolet regularized pair interaction as previously studied in Gebert et al. (Ann Henri Poincaré 21(11):3609–3637, 2020). We provide a Lieb–Robinson bound under substantially relaxed assumptions on the potentials. We also improve the associated one-body Lieb–Robinson bound on $$L^2$$ L 2 -overlaps to an almost ballistic one (i.e., an almost linear light cone) under the same relaxed assumptions. Applications include the existence of the infinite-volume dynamics and clustering of ground stat

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21

Ranard, Daniel, Michael Walter, and Freek Witteveen. "A Converse to Lieb–Robinson Bounds in One Dimension Using Index Theory." Annales Henri Poincaré, July 26, 2022. http://dx.doi.org/10.1007/s00023-022-01193-x.

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AbstractUnitary dynamics with a strict causal cone (or “light cone”) have been studied extensively, under the name of quantum cellular automata (QCAs). In particular, QCAs in one dimension have been completely classified by an index theory. Physical systems often exhibit only approximate causal cones; Hamiltonian evolutions on the lattice satisfy Lieb–Robinson bounds rather than strict locality. This motivates us to study approximately locality preserving unitaries (ALPUs). We show that the index theory is robust and completely extends to one-dimensional ALPUs. As a consequence, we achieve a c

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22

Huang, Zhiqiang, and Xiao-Kan Guo. "Lieb-Robinson bound at finite temperatures." Physical Review E 97, no. 6 (2018). http://dx.doi.org/10.1103/physreve.97.062131.

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23

Fu, Hao, Mingqiu Luo, and Peiqing Tong. "Lieb-Robinson bound in one-dimensional inhomogeneous quantum systems." Physica B: Condensed Matter, April 2022, 413958. http://dx.doi.org/10.1016/j.physb.2022.413958.

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24

Fu, Hao, Mingqiu Luo, and Peiqing Tong. "Lieb-Robinson bound in one-dimensional inhomogeneous quantum systems." Physica B: Condensed Matter, April 2022, 413958. http://dx.doi.org/10.1016/j.physb.2022.413958.

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25

Fu, Hao, Peiqing Tong, and Mingqiu Luo. "Lieb-Robinson Bound in One-Dimensional Inhomogeneous Quantum Systems." SSRN Electronic Journal, 2022. http://dx.doi.org/10.2139/ssrn.4053161.

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26

Wang, Zhiyuan, and Kaden R. A. Hazzard. "Tightening the Lieb-Robinson Bound in Locally Interacting Systems." PRX Quantum 1, no. 1 (2020). http://dx.doi.org/10.1103/prxquantum.1.010303.

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27

Poulin, David. "Lieb-Robinson Bound and Locality for General Markovian Quantum Dynamics." Physical Review Letters 104, no. 19 (2010). http://dx.doi.org/10.1103/physrevlett.104.190401.

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28

Braida, Arthur, Simon Martiel, and Ioan Todinca. "Tight Lieb–Robinson Bound for approximation ratio in quantum annealing." npj Quantum Information 10, no. 1 (2024). http://dx.doi.org/10.1038/s41534-024-00832-x.

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AbstractQuantum annealing (QA) holds promise for optimization problems in quantum computing, especially for combinatorial optimization. This analog framework attracts attention for its potential to address complex problems. Its gate-based homologous, QAOA with proven performance, has attracted a lot of attention to the NISQ era. Several numerical benchmarks try to compare these two metaheuristics, however, classical computational power highly limits the performance insights. In this work, we introduce a parametrized version of QA enabling a precise 1-local analysis of the algorithm. We develop

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29

Ampelogiannis, Dimitrios, and Benjamin Doyon. "Clustering of higher order connected correlations in C* dynamical systems." Journal of Mathematical Physics 66, no. 5 (2025). https://doi.org/10.1063/5.0233610.

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In the context of C* dynamical systems, we consider a locally compact group G acting by *-automorphisms on a C* algebra U of observables, and assume a state of U that satisfies the clustering property with respect to a net of group elements of G. That is, the two-point connected correlation function vanishes in the limit on the net, when one observable is translated under the group action. Then we show that all higher order connected correlation functions (Ursell functions, or classical cumulants) and all free correlation functions (free cumulants, from free probability) vanish at the same rat

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30

Kuwahara, Tomotaka, Tan Van Vu, and Keiji Saito. "Effective light cone and digital quantum simulation of interacting bosons." Nature Communications 15, no. 1 (2024). http://dx.doi.org/10.1038/s41467-024-46501-7.

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AbstractThe speed limit of information propagation is one of the most fundamental features in non-equilibrium physics. The region of information propagation by finite-time dynamics is approximately restricted inside the effective light cone that is formulated by the Lieb-Robinson bound. To date, extensive studies have been conducted to identify the shape of effective light cones in most experimentally relevant many-body systems. However, the Lieb-Robinson bound in the interacting boson systems, one of the most ubiquitous quantum systems in nature, has remained a critical open problem for a lon

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31

Roberts, Daniel A., and Brian Swingle. "Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories." Physical Review Letters 117, no. 9 (2016). http://dx.doi.org/10.1103/physrevlett.117.091602.

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32

Abeling, Nils O., Lorenzo Cevolani, and Stefan Kehrein. "Analysis of the buildup of spatiotemporal correlations and their bounds outside of the light cone." SciPost Physics 5, no. 5 (2018). http://dx.doi.org/10.21468/scipostphys.5.5.052.

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In non-relativistic quantum theories the Lieb-Robinson bound defines an effective light cone with exponentially small tails outside of it. In this work we use it to derive a bound for the correlation function of two local disjoint observables at different times if the initial state has a power-law decay. We show that the exponent of the power-law of the bound is identical to the initial (equilibrium) decay. We explicitly verify this result by studying the full dynamics of the susceptibilities and correlations in the exactly solvable Luttinger model after a sudden quench from the non-interactin

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33

Jameson, Casey, Bora Basyildiz, Daniel Moore, Kyle Clark, and Zhexuan Gong. "Time optimal quantum state transfer in a fully-connected quantum computer." Quantum Science and Technology, October 26, 2023. http://dx.doi.org/10.1088/2058-9565/ad0770.

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Abstract The speed limit of quantum state transfer (QST) in a system of interacting particles is not only important for quantum information processing, but also directly linked to Lieb-Robinson-type bounds that are crucial for understanding various aspects of quantum many-body physics. For strongly long-range interacting systems such as a fully-connected quantum computer, such a speed limit is still unknown. Here we develop a new Quantum Brachistochrone method that can incorporate inequality constraints on the Hamiltonian. This method allows us to prove an exactly tight bound on the speed of Q

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34

Gebert, Martin, Alvin Moon, and Bruno Nachtergaele. "A Lieb–Robinson bound for quantum spin chains with strong on-site impurities." Reviews in Mathematical Physics, January 15, 2022. http://dx.doi.org/10.1142/s0129055x22500076.

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We consider a quantum spin chain with nearest neighbor interactions and sparsely distributed on-site impurities. We prove commutator bounds for its Heisenberg dynamics which incorporate the coupling strengths of the impurities. The impurities are assumed to satisfy a minimum spacing, and each impurity has a non-degenerate spectrum. Our results are proven in a broadly applicable setting, both in finite volume and in thermodynamic limit. We apply our results to improve Lieb–Robinson bounds for the Heisenberg spin chain with a random, sparse transverse field drawn from a heavy-tailed distribution

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35

Kuwahara, Tomotaka, and Keiji Saito. "Lieb-Robinson Bound and Almost-Linear Light Cone in Interacting Boson Systems." Physical Review Letters 127, no. 7 (2021). http://dx.doi.org/10.1103/physrevlett.127.070403.

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36

Else, Dominic V., Francisco Machado, Chetan Nayak, and Norman Y. Yao. "Improved Lieb-Robinson bound for many-body Hamiltonians with power-law interactions." Physical Review A 101, no. 2 (2020). http://dx.doi.org/10.1103/physreva.101.022333.

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37

Nickelsen, Daniel, and Michael Kastner. "Classical Lieb-Robinson Bound for Estimating Equilibration Timescales of Isolated Quantum Systems." Physical Review Letters 122, no. 18 (2019). http://dx.doi.org/10.1103/physrevlett.122.180602.

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38

Gong, Zongping, Tommaso Guaita, and J. Ignacio Cirac. "Long-Range Free Fermions: Lieb-Robinson Bound, Clustering Properties, and Topological Phases." Physical Review Letters 130, no. 7 (2023). http://dx.doi.org/10.1103/physrevlett.130.070401.

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39

Shiraishi, Naoto, and Hiroyasu Tajima. "Efficiency versus speed in quantum heat engines: Rigorous constraint from Lieb-Robinson bound." Physical Review E 96, no. 2 (2017). http://dx.doi.org/10.1103/physreve.96.022138.

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40

Shiraishi, Koki, Masaya Nakagawa, Takashi Mori, and Masahito Ueda. "Quantum master equation for many-body systems based on the Lieb-Robinson bound." Physical Review B 111, no. 18 (2025). https://doi.org/10.1103/physrevb.111.184311.

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41

Chen, Xiao, Yingfei Gu, and Andrew Lucas. "Many-body quantum dynamics slows down at low density." SciPost Physics 9, no. 5 (2020). http://dx.doi.org/10.21468/scipostphys.9.5.071.

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We study quantum many-body systems with a global U(1) conservation law, focusing on a theory of N interacting fermions with charge conservation, or N interacting spins with one conserved component of total spin. We define an effective operator size at finite chemical potential through suitably regularized out-of-time-ordered correlation functions. The growth rate of this density-dependent operator size vanishes algebraically with charge density; hence we obtain new bounds on Lyapunov exponents and butterfly velocities in charged systems at a given density, which are parametrically stronger tha

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42

Gong, Zongping, and Ryusuke Hamazaki. "Bounds in nonequilibrium quantum dynamics." International Journal of Modern Physics B, September 26, 2022. http://dx.doi.org/10.1142/s0217979222300079.

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We review various bounds concerning out-of-equilibrium dynamics in few-level and many-body quantum systems. We primarily focus on closed quantum systems but will also mention some related results for open quantum systems and classical stochastic systems. We start from the speed limits, the universal bounds on the speeds of (either quantum or classical) dynamical evolutions. We then turn to review the bounds that address how good and how long would a quantum system equilibrate or thermalize. Afterward, we focus on the stringent constraint set by locality in many-body systems, rigorously formali

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Ageev, Dmitry S., Andrey A. Bagrov, Aleksandr I. Belokon, Askar Iliasov, Vasilii V. Pushkarev, and Femke Verheijen. "Local quenches in fracton field theory: Lieb-Robinson bound, noncausal dynamics and fractal excitation patterns." Physical Review D 110, no. 6 (2024). http://dx.doi.org/10.1103/physrevd.110.065011.

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We study the out-of-equilibrium dynamics induced by a local perturbation in fracton field theory. For the Z4- and Z8-symmetric free fractonic theories, we compute the time dynamics of several observables such as the two-point Green’s function, ⟨ϕ2⟩ condensate, energy density, and the dipole momentum. The time-dependent considerations highlight that the free fractonic theory breaks causality and exhibits instantaneous signal propagation, even if an additional relativistic term is included to enforce a speed limit in the system. We show that it is related to the fact that the Lieb-Robinson bound

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Braida, Arthur, Simon Martiel, and Ioan Todinca. "On constant-time quantum annealing and guaranteed approximations for graph optimization problems." Quantum Science and Technology, September 1, 2022. http://dx.doi.org/10.1088/2058-9565/ac8e91.

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Abstract Quantum Annealing (QA) is a computational framework where a quantum system’s continuous evolution is used to ﬁnd the global minimum of an objective function over an unstructured search space. It can be seen as a general metaheuristic for optimization problems, including NP-hard ones if we allow an exponentially large running time. While QA is widely studied from a heuristic point of view, little is known about theoretical guarantees on the quality of the solutions obtained in polynomial time. In this paper, we use a technique borrowed from theoretical physics, the Lieb-Robinson (LR) b

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45

Ampelogiannis, Dimitrios, and Benjamin Doyon. "Long-Time Dynamics in Quantum Spin Lattices: Ergodicity and Hydrodynamic Projections at All Frequencies and Wavelengths." Annales Henri Poincaré, May 5, 2023. http://dx.doi.org/10.1007/s00023-023-01304-2.

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AbstractObtaining rigorous and general results about the non-equilibrium dynamics of extended many-body systems is a difficult task. In quantum lattice models with short-range interactions, the Lieb–Robinson bound tells us that the spatial extent of operators grows at most linearly in time. But what happens within this light-cone? We discuss rigorous results on ergodicity and the emergence of the Euler hydrodynamic scale in correlation functions, which establish fundamental principles at the root of non-equilibrium physics. One key idea of the present work is that general structures of Euler h

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46

TONONI, ANDREA, and Maciej Lewenstein. "Temporal Bell inequalities in non-relativistic many-body physics." Quantum Science and Technology, April 11, 2025. https://doi.org/10.1088/2058-9565/adcbce.

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Abstract Analyzing the spreading of information in many-body systems is crucial to understanding their quantum dynamics. At the most fundamental level, this task is accomplished by Bell inequalities, whose violation by quantum mechanics implies that information cannot always be stored locally. While Bell-like inequalities, such as the one of Clauser and Horne, envisage a situation in which two parties perform measurements on systems at different positions, one could formulate temporal inequalities, in which the two parties measure at different times. However, for causally-connected measurement

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47

Ponnaganti, Ravi Teja, Matthieu Mambrini, and Didier Poilblanc. "Tensor network variational optimizations for real-time dynamics: Application to the time-evolution of spin liquids." SciPost Physics 15, no. 4 (2023). http://dx.doi.org/10.21468/scipostphys.15.4.158.

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Within the Projected Entangled Pair State (PEPS) tensor network formalism, a simple update (SU) method has been used to investigate the time evolution of a two-dimensional U(1) critical spin-1/2 spin liquid under Hamiltonian quench [Phys. Rev. B 106, 195132 (2022)]. Here we introduce two different variational frameworks to describe the time dynamics of SU(2)-symmetric translationally-invariant PEPS, aiming to improve the accuracy. In one approach, after using a Trotter-Suzuki decomposition of the time evolution operator in term of two-site elementary gates, one considers a single bond embedded

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Ampelogiannis, Dimitrios, and Benjamin Doyon. "Almost Everywhere Ergodicity in Quantum Lattice Models." Communications in Mathematical Physics, October 30, 2023. http://dx.doi.org/10.1007/s00220-023-04849-9.

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AbstractWe rigorously examine, in generality, the ergodic properties of quantum lattice models with short range interactions, in the $$C^*$$ C ∗ algebra formulation of statistical mechanics. Ergodicity results, in the context of group actions on $$C^*$$ C ∗ algebras, assume that the algebra is asymptotically abelian, which is not generically the case for time evolution. The Lieb-Robinson bound tells us that, in a precise sense, the spatial extent of any time-evolved local operator grows linearly with time. This means that the algebra of observables is asymptotically abelian in a space-like reg

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Wilming, Henrik, and Albert H. Werner. "Lieb-Robinson bounds imply locality of interactions." Physical Review B 105, no. 12 (2022). http://dx.doi.org/10.1103/physrevb.105.125101.

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Damanik, David, Marius Lemm, Milivoje Lukic, and William Yessen. "New Anomalous Lieb-Robinson Bounds in QuasiperiodicXYChains." Physical Review Letters 113, no. 12 (2014). http://dx.doi.org/10.1103/physrevlett.113.127202.

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