General theory of many body localized systems coupled to baths

TL;DR

This paper develops a comprehensive theoretical framework for understanding how many-body localized systems interact with various types of heat baths, revealing new quantum regimes and phase diagrams beyond previous models.

Contribution

It introduces a unified analysis of coupled many-body localized systems and baths, including quantum effects, different bath regimes, and boundary scenarios, expanding beyond prior simplified models.

Findings

Identifies regimes where bath effects are classical noise or quantum.

Discovers a new quantum regime of system-bath interaction.

Maps the phase diagram of coupled MBL systems and baths.

Abstract

We consider what happens when a many body localized system is coupled to a heat bath. Unlike previous works, we do not restrict ourselves to the limit where the bath is large and effectively Markovian, nor to the limit where back action on the bath is negligible. We identify limits where the effect of the bath can be captured by classical noise, and limits where it cannot. We also identify limits in which the bath delocalizes the system, as well as limits in which the system localizes the bath. Using general arguments and dimensional analysis, we constrain the overall phase diagram of the coupled system and bath. Our analysis incorporates all the previously discussed regimes, and also uncovers a new intrinsically quantum regime that has not hitherto been discussed. We discuss baths that are themselves near a localization transition, or are strongly disordered but protected against localization by symmetry or topology. We also discuss situations where the system and bath have different dimensionality (the case of `boundary MBL' and `boundary baths').