Chaos and Information Scrambling in Many-body Quantum Systems

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.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:1712.08813Physical review. B./Physical review. BJul 2, 201831 citations

Scrambling and onset of chaos in quantum many-body systems

Debanjan Chowdhury, Brian G. Swingle

Bulletin of the American Physical SocietyMar 13, 20170 citations

Information Scrambling and Chaos in Graphene

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

We determine the information scrambling rate $\lambda_{L}$ due to electron-electron Coulomb interaction in graphene. $\lambda_{L}$ characterizes the growth of chaos and gives information about the thermalization of a many body system. We demonstrate that $\lambda_{L}$ behaves for strong coupling similar to transport scattering rates. A weak coupling analysis however reveals that scrambling is related to dephasing or single particle relaxation, and that $\lambda_{L}$ is parametrically larger than the collision time relevant for hydrodynamic processes such as electrical conduction and viscous flow.We determine the information scrambling rate $\lambda_{L}$ due to electron-electron Coulomb interaction in graphene. $\lambda_{L}$ characterizes the growth of chaos and gives information about the thermalization of a many body system. We demonstrate that $\lambda_{L}$ behaves for strong coupling similar to transport scattering rates. A weak coupling analysis however reveals that scrambling is related to dephasing or single particle relaxation, and that $\lambda_{L}$ is parametrically larger than the collision time relevant for hydrodynamic processes such as electrical conduction and viscous flow.

Dec 23, 20170 citations

Chaos in quantum many-body systems

Gary E. Mitchell

Bulletin of the American Physical SocietyOct 28, 20061 citation

Information scrambling in all-to-all interacting models

Abhik Kumar Saha, Tanay Pathak, Masaki Tezuka

Information scrambling is a hallmark of quantum chaos and thermalization in isolated quantum many-body systems. We investigate scrambling dynamics in the all-to-all interacting spin Sachdev-Ye-Kitaev (SYK)- $q$ model using both pure- and mixed-state entanglement measures. We show that von-Neumann and Rényi entropies exhibit rapid growth followed by saturation near Haar-random values, signaling efficient scrambling. The scrambling rate reveals a nontrivial dependence on the interaction order, system size, and Hamiltonian scaling. We further employ mixed-state entanglement as a powerful probe of information scrambling. We numerically find a universal relation between the Rényi-1/2 mutual information and entanglement negativity for minimal interaction order in the early growth regime. Furthermore, entanglement negativity displays a Page-curve-like behavior under unequal subsystem partitioning, characterized by the birth, spread, and eventual death of quantum correlations. Our results provide a generic description of information scrambling using entanglement dynamics in all-to-all interacting spin systems with multi-body interactions.Information scrambling is a hallmark of quantum chaos and thermalization in isolated quantum many-body systems. We investigate scrambling dynamics in the all-to-all interacting spin Sachdev-Ye-Kitaev (SYK)-$q$ model using both pure- and mixed-state entanglement measures. We show that von-Neumann and Rényi entropies exhibit rapid growth followed by saturation near Haar-random values, signaling efficient scrambling. The scrambling rate reveals a nontrivial dependence on the interaction order, system size, and Hamiltonian scaling. We further employ mixed-state entanglement as a powerful probe of information scrambling. We numerically find a universal relation between the Rényi-1/2 mutual information and entanglement negativity for minimal interaction order in the early growth regime. Furthermore, entanglement negativity displays a Page-curve-like behavior under unequal subsystem partitioning, characterized by the birth, spread, and eventual death of quantum correlations. Our results provide a generic description of information scrambling using entanglement dynamics in all-to-all interacting spin systems with multi-body interactions.

quant-pharXiv:2606.02207Jun 2, 20260 citations

Observation of Thermalization and Information Scrambling in a Superconducting Quantum Processor

Qingling Zhu, Zheng‐Hang Sun, Ming Gong +22 more

Understanding various phenomena in nonequilibrium dynamics of closed quantum many-body systems, such as quantum thermalization, information scrambling, and nonergodic dynamics, is crucial for modern physics. Using a ladder-type superconducting quantum processor, we perform analog quantum simulations of both the XX-ladder model and the one-dimensional XX model. By measuring the dynamics of local observables, entanglement entropy, and tripartite mutual information, we signal quantum thermalization and information scrambling in the XX ladder. In contrast, we show that the XX chain, as free fermions on a one-dimensional lattice, fails to thermalize to the Gibbs ensemble, and local information does not scramble in the integrable channel. Our experiments reveal ergodicity and scrambling in the controllable qubit ladder, and open the door to further investigations on the thermodynamics and chaos in quantum many-body systems.Understanding various phenomena in nonequilibrium dynamics of closed quantum many-body systems, such as quantum thermalization, information scrambling, and nonergodic dynamics, is crucial for modern physics. Using a ladder-type superconducting quantum processor, we perform analog quantum simulations of both the XX-ladder model and the one-dimensional XX model. By measuring the dynamics of local observables, entanglement entropy, and tripartite mutual information, we signal quantum thermalization and information scrambling in the XX ladder. In contrast, we show that the XX chain, as free fermions on a one-dimensional lattice, fails to thermalize to the Gibbs ensemble, and local information does not scramble in the integrable channel. Our experiments reveal ergodicity and scrambling in the controllable qubit ladder, and open the door to further investigations on the thermodynamics and chaos in quantum many-body systems.

arXiv:2101.08031Physical Review LettersApr 19, 202257 citations

We determine the information scrambling rate

\lambda_{L}

due to electron-electron Coulomb interaction in graphene.

\lambda_{L}

characterizes the growth of chaos and gives information about the thermalization of a many body system. We demonstrate that

\lambda_{L}

behaves for strong coupling similar to transport scattering rates. A weak coupling analysis however reveals that scrambling is related to dephasing or single particle relaxation, and that

\lambda_{L}

is parametrically larger than the collision time relevant for hydrodynamic processes such as electrical conduction and viscous flow.

q

model using both pure- and mixed-state entanglement measures. We show that von-Neumann and Rényi entropies exhibit rapid growth followed by saturation near Haar-random values, signaling efficient scrambling. The scrambling rate reveals a nontrivial dependence on the interaction order, system size, and Hamiltonian scaling. We further employ mixed-state entanglement as a powerful probe of information scrambling. We numerically find a universal relation between the Rényi-1/2 mutual information and entanglement negativity for minimal interaction order in the early growth regime. Furthermore, entanglement negativity displays a Page-curve-like behavior under unequal subsystem partitioning, characterized by the birth, spread, and eventual death of quantum correlations. Our results provide a generic description of information scrambling using entanglement dynamics in all-to-all interacting spin systems with multi-body interactions.