Signatures of chaos and thermalization in the dynamics of many-body quantum systems

TL;DR

This paper investigates quantum chaos and thermalization in many-body quantum systems, providing numerical evidence for algebraic decay behaviors and the correlation hole in observables, bridging theoretical predictions with experimental relevance.

Contribution

It extends previous work by numerically confirming the onset of algebraic decay and analyzing the correlation hole in both chaotic and many-body localized regimes.

Findings

Power-law decay of survival probability indicates thermalization.

Correlation hole appears in chaotic and localized regimes.

Observable dynamics reflect signatures of quantum chaos.

Abstract

We extend the results of two of our papers [Phys. Rev. A 94, 041603R (2016) and Phys. Rev. B 97, 060303R (2018)] that touch upon the intimately connected topics of quantum chaos and thermalization. In the first, we argued that when the initial state of isolated lattice many-body quantum systems is chaotic, the power-law decay of the survival probability is caused by the bounds in the spectrum, and thus anticipates thermalization. In the current work, we provide stronger numerical support for the onset of these algebraic behaviors. In the second paper, we demonstrated that the correlation hole, which is a direct signature of quantum chaos revealed by the evolution of the survival probability at times beyond the power-law decay, appears also for other observables. In the present work, we investigate the correlation hole in the chaotic regime and in the vicinity of a many-body localized phase for the spin density imbalance, which is an observable studied experimentally.