Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1705.08910 · Physical Review X

Operator Hydrodynamics, OTOCs, and Entanglement Growth in Systems without Conservation Laws

Curt W. von Keyserlingk, Tibor Rakovszky, Frank Pollmann, S. L. Sondhi

Published Apr 11, 2018• 589 citations
arXivHTMLPDF

Abstract

Thermalization and information scrambling can provide insight into fields as diverse as many-body quantum physics, quantum field theory, and holography. A new theoretical analysis of one-dimensional spin chains reveals details about how information moves and entanglement grows in such systems.
DOI
10.1103/physrevx.8.021013

Related papers

Entanglement structure in quantum many-body systems, field theories, and holography

森 崇人, タカト モリ, Takato Mori

•Mar 24, 2023•0 citations

Information Scrambling with Conservation Laws

Jonah Kudler-Flam, Ramanjit Sohal, Laimei Nie

The delocalization or scrambling of quantum information has emerged as a central ingredient in the understanding of thermalization in isolated quantum many-body systems. Recently, significant progress has been made analytically by modeling non-integrable systems as periodically driven systems, lacking a Hamiltonian picture, while honest Hamiltonian dynamics are frequently limited to small system sizes due to computational constraints. In this paper, we address this by investigating the role of conservation laws (including energy conservation) in the thermalization process from an information-theoretic perspective. For general non-integrable models, we use the equilibrium approximation to show that the maximal amount of information is scrambled (as measured by the tripartite mutual information of the time-evolution operator) at late times even when a system conserves energy. In contrast, we explicate how when a system has additional symmetries that lead to degeneracies in the spectrum, the amount of information scrambled must decrease. This general theory is exemplified in case studies of holographic conformal field theories (CFTs) and the Sachdev-Ye-Kitaev (SYK) model. Due to the large Virasoro symmetry in 1+1D CFTs, we argue that, in a sense, these holographic theories are not maximally chaotic, which is explicitly seen by the non-saturation of the second Rényi tripartite mutual information. The roles of particle-hole and U(1) symmetries in the SYK model are milder due to the degeneracies being only two-fold, which we confirm explicitly at both large- and small-N. We reinterpret the operator entanglement in terms of the growth of local operators, connecting our results with the information scrambling described by out-of-time-ordered correlators, identifying the mechanism for suppressed scrambling from the Heisenberg perspective.

arXiv:2107.04043•SciPost Physics•Apr 4, 2022•17 citations

Entanglement in many-body quantum systems

J. I. Cirac

Short review on entanglement, as seen from a quantum information perspective, and some simple applications to many-body quantum systems. Special emphasis in area laws, cold atoms, and efficient descriptions using tensor network states.

arXiv:1205.3742•May 16, 2012•1 citation

Information Scrambling in Quantum Many-Body Systems

Yongliang Zhang

A closed quantum system never forgets its initial state, but the encoded information can get scrambled and become inaccessible without measuring a large fraction of all the system degrees of freedom. This scrambling can be diagnosed by studying the spatial spreading of initially local operators under the Heisenberg time evolution, and the decay of the out-of-time-ordered correlators (OTOC). What insights can OTOCs provide to understand the dynamics of quantum many-body systems? What are the characteristic behaviors of OTOCs during the time evolution? How is information scrambling affected by the dissipation in open quantum many-body systems? We first study slow scrambling in many-body localized systems via calculating various correlators, two-point retarded correlators and OTOCs. Comparing with retarded correlators, OTOCs provide more information about the dynamics. We find that disorder slows and partially halts the onset of information scrambling. Instead of ballistic spreading, propagation of information forms a logarithmic light cone. Next, we study the finite-size scaling of OTOCs at late times in generic thermalizing quantum many-body systems. When energy is conserved, the late-time saturation value of the OTOC of generic traceless local operators scales as an inverse polynomial in the system size. This is in contrast to the inverse exponential scaling expected for chaotic dynamics without energy conservation. We also study information scrambling in open quantum many-body systems. We define a dissipative version of OTOC and study its behaviors in a prototypical chaotic quantum chain with dissipation. We find that dissipation leads to not only the overall decay of the scrambled information due to leaking, but also structural changes so that the information light cone can only reach a finite distance even when the effect of overall decay is removed. Finally, we construct a family of local Hamiltonians for understanding the asymmetric information scrambling. Our models live on a one-dimensional lattice and exhibit asymmetric butterfly light cone between the left and right spatial directions.

•Feb 28, 2020•5 citations

Hierarchy of information scrambling, thermalization, and hydrodynamic flow in graphene

Markus J. Klug, Mathias S. Scheurer, Jörg Schmalian

We determine the information scrambling rate ${\ensuremath{\lambda}}_{L}$ due to electron-electron Coulomb interaction in graphene. ${\ensuremath{\lambda}}_{L}$ characterizes the growth of chaos and has been argued to give information about the thermalization and hydrodynamic transport coefficients of a many-body system. We demonstrate that ${\ensuremath{\lambda}}_{L}$ behaves for strong coupling similar to transport and energy relaxation rates. A weak coupling analysis, however, reveals that scrambling is related to dephasing or single-particle relaxation. Furthermore, ${\ensuremath{\lambda}}_{L}$ is found to be parametrically larger than the collision rate relevant for hydrodynamic processes, such as electrical conduction or viscous flow, and the rate of energy relaxation, relevant for thermalization. Thus, while scrambling is obviously necessary for thermalization and quantum transport, it does generically not set the timescale for these processes. In addition, we derive a quantum kinetic theory for information scrambling that resembles the celebrated Boltzmann equation and offers a physically transparent insight into quantum chaos in many-body systems.

arXiv:1712.08813•Physical review. B./Physical review. B•Jul 2, 2018•31 citations

Entanglement and tensor network states

Jens Eisert

These lecture notes provide a brief overview of methods of entanglement theory applied to the study of quantum many-body systems, as well as of tensor network states capturing quantum states naturally appearing in condensed-matter systems.

arXiv:1308.3318•Aug 15, 2013•53 citations
The delocalization or scrambling of quantum information has emerged as a central ingredient in the understanding of thermalization in isolated quantum many-body systems. Recently, significant progress has been made analytically by modeling non-integrable systems as periodically driven systems, lacking a Hamiltonian picture, while honest Hamiltonian dynamics are frequently limited to small system sizes due to computational constraints. In this paper, we address this by investigating the role of conservation laws (including energy conservation) in the thermalization process from an information-theoretic perspective. For general non-integrable models, we use the equilibrium approximation to show that the maximal amount of information is scrambled (as measured by the tripartite mutual information of the time-evolution operator) at late times even when a system conserves energy. In contrast, we explicate how when a system has additional symmetries that lead to degeneracies in the spectrum, the amount of information scrambled must decrease. This general theory is exemplified in case studies of holographic conformal field theories (CFTs) and the Sachdev-Ye-Kitaev (SYK) model. Due to the large Virasoro symmetry in 1+1D CFTs, we argue that, in a sense, these holographic theories are not maximally chaotic, which is explicitly seen by the non-saturation of the second Rényi tripartite mutual information. The roles of particle-hole and U(1) symmetries in the SYK model are milder due to the degeneracies being only two-fold, which we confirm explicitly at both large- and small-N. We reinterpret the operator entanglement in terms of the growth of local operators, connecting our results with the information scrambling described by out-of-time-ordered correlators, identifying the mechanism for suppressed scrambling from the Heisenberg perspective.
A closed quantum system never forgets its initial state, but the encoded information can get scrambled and become inaccessible without measuring a large fraction of all the system degrees of freedom. This scrambling can be diagnosed by studying the spatial spreading of initially local operators under the Heisenberg time evolution, and the decay of the out-of-time-ordered correlators (OTOC). What insights can OTOCs provide to understand the dynamics of quantum many-body systems? What are the characteristic behaviors of OTOCs during the time evolution? How is information scrambling affected by the dissipation in open quantum many-body systems? We first study slow scrambling in many-body localized systems via calculating various correlators, two-point retarded correlators and OTOCs. Comparing with retarded correlators, OTOCs provide more information about the dynamics. We find that disorder slows and partially halts the onset of information scrambling. Instead of ballistic spreading, propagation of information forms a logarithmic light cone. Next, we study the finite-size scaling of OTOCs at late times in generic thermalizing quantum many-body systems. When energy is conserved, the late-time saturation value of the OTOC of generic traceless local operators scales as an inverse polynomial in the system size. This is in contrast to the inverse exponential scaling expected for chaotic dynamics without energy conservation. We also study information scrambling in open quantum many-body systems. We define a dissipative version of OTOC and study its behaviors in a prototypical chaotic quantum chain with dissipation. We find that dissipation leads to not only the overall decay of the scrambled information due to leaking, but also structural changes so that the information light cone can only reach a finite distance even when the effect of overall decay is removed. Finally, we construct a family of local Hamiltonians for understanding the asymmetric information scrambling. Our models live on a one-dimensional lattice and exhibit asymmetric butterfly light cone between the left and right spatial directions.
We determine the information scrambling rate ${\ensuremath{\lambda}}_{L}$ due to electron-electron Coulomb interaction in graphene. ${\ensuremath{\lambda}}_{L}$ characterizes the growth of chaos and has been argued to give information about the thermalization and hydrodynamic transport coefficients of a many-body system. We demonstrate that ${\ensuremath{\lambda}}_{L}$ behaves for strong coupling similar to transport and energy relaxation rates. A weak coupling analysis, however, reveals that scrambling is related to dephasing or single-particle relaxation. Furthermore, ${\ensuremath{\lambda}}_{L}$ is found to be parametrically larger than the collision rate relevant for hydrodynamic processes, such as electrical conduction or viscous flow, and the rate of energy relaxation, relevant for thermalization. Thus, while scrambling is obviously necessary for thermalization and quantum transport, it does generically not set the timescale for these processes. In addition, we derive a quantum kinetic theory for information scrambling that resembles the celebrated Boltzmann equation and offers a physically transparent insight into quantum chaos in many-body systems.