Self-averaging in many-body quantum systems out of equilibrium. II. Approach to the localized phase

TL;DR

This paper investigates how self-averaging properties of many-body quantum systems change out of equilibrium as they transition to the localized phase, revealing that local observables become self-averaging while non-local ones do not.

Contribution

It provides a detailed analysis of self-averaging behavior out of equilibrium in the localized phase, using models to explain observable-dependent differences.

Findings

Local observables become self-averaging at all times in the localized phase.

Non-local quantities remain non-self-averaging throughout.

Scaling analysis supports the observed behaviors.

Abstract

The self-averaging behavior of interacting many-body quantum systems has been mostly studied at equilibrium. The present work addresses what happens out of equilibrium, as the increase of the strength of onsite disorder takes the system to the localized phase. We consider two local and two non-local quantities of great experimental and theoretical interest. In the delocalized phase, self-averaging depends on the observable and on the time scale, but the picture simplifies substantially when localization is reached. In the localized phase, the local observables become self-averaging at all times, while the non-local quantities are throughout non-self-averaging. These behaviors are explained and scaling analysis are provided using the $\ell$-bits model and a toy model.