Chaos and High Temperature Pure State Thermalization

TL;DR

This paper explores the relationship between quantum chaos and thermalization in many-body systems, showing that suppressed mutual information indicates rapid entanglement growth and thermalization.

Contribution

It introduces a new criterion linking quantum chaos to entanglement entropy growth via mutual information suppression in unitary evolution.

Findings

Small mutual information correlates with rapid entanglement growth.

Unentangled initial states evolve into highly entangled states under chaotic dynamics.

Provides a concrete connection between quantum chaos and 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.