Chaos and High Temperature Pure State Thermalization

Abstract

Classical arguments for thermalization of isolated systems do not apply in a straightforward way to the quantum case. Recently, there has been interest in diagnostics of quantum chaos in many- body systems. In the classical case, chaos is a popular explanation for the legitimacy of the methods of statistical physics. In this work, we relate a previously proposed criteria of quantum chaos in the unitary time evolution operator to the entanglement entropy growth for a far-from-equilibrium initial pure state. By mapping the unitary time evolution operator to a doubled state, chaos can be characterized by suppression of mutual information between subsystems of the past and that of the future. We show that when this mutual information is small, a typical unentangled initial state will evolve to a highly entangled final state. Our result provides a more concrete connection between quantum chaos and thermalization in many-body systems.

arXiv comment17 pages, 2 figures; added reference and fixed typo in appendix

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• Quantifying information scrambling via Classical Shadow Tomography on Programmable Quantum Simulators
• Scrambling and operator entanglement in local non-Hermitian quantum systems
• Multi-Region Entanglement in Locally Scrambled Quantum Dynamics
• Scrambling in Yang-Mills
• Entanglement Dynamics From Random Product States: Deviation From Maximal Entanglement
• Adding boundary terms to Anderson localized Hamiltonians leads to unbounded growth of entanglement
• Long-time properties of generic Floquet systems are approximately periodic with the driving period
• Diagnosing chaos with projected ensembles of process tensors