Many-body localization in the presence of a small bath

TL;DR

This paper investigates how a small bath influences many-body localization, revealing that interactions typically delocalize the system, but certain conditions can preserve localization, highlighting the many-body proximity effect.

Contribution

It introduces a model with coexisting localized and delocalized degrees of freedom and analyzes how interactions affect localization, providing insights into the many-body proximity effect.

Findings

Interactions generally delocalize the system

Certain parameter regimes maintain localization

Numerical and analytical evidence supports the proximity effect

Abstract

In the presence of strong disorder and weak interactions, closed quantum systems can enter a many-body localized phase where the system does not conduct, does not equilibrate even for arbitrarily long times, and robustly violates quantum statistical mechanics. The starting point for such a many-body localized phase is usually taken to be an Anderson insulator where, in the limit of vanishing interactions, all degrees of freedom of the system are localized. Here, we instead consider a model where in the non-interacting limit, some degrees of freedom are localized while others remain delocalized. Such a system can be viewed as a model for a many-body localized system brought into contact with a small bath of a comparable number of degrees of freedom. We numerically and analytically study the effect of interactions on this system and find that generically, the entire system delocalizes. However, we find certain parameter regimes where results are consistent with localization of the entire system, an effect recently termed many-body proximity effect.