Stability and Dynamics of Many-Body Localized Systems Coupled to Small Bath

TL;DR

This study investigates how a disordered quantum spin chain's many-body localization is affected by coupling to a finite environment, revealing that localization generally persists but can vary with coupling strength, geometry, and initial states.

Contribution

It provides a detailed analysis of the stability of many-body localization in finite system-environment setups, highlighting conditions that preserve or destroy localization.

Findings

Localization persists despite finite environment coupling

Strong system-environment coupling can lead to thermalization

Initial state influences localization outcomes in ladder configurations

Abstract

It is known that strong disorder in closed quantum systems leads to many-body localization (MBL), and that this quantum phase can be destroyed by coupling to an infinitely large Markovian environment. However, the stability of the MBL phase is less clear when the system and environment are of finite and comparable size. Here, we study the stability and eventual localization properties of a disordered Heisenberg spin chain coupled to a finite environment, and extensively explore the effects of environment disorder, geometry, initial state and system-bath coupling strength. By studying the non-equilibrium dynamics and the eventual steady-state properties of different initial states, our numerical results indicate that in most cases, the system retains its localization properties despite the coupling to the finite environment, albeit to a reduced extent. However, in cases where the system and environment is strongly coupled in the ladder configuration, the eventual localization properties are highly dependent on the initial state, and could lead to either thermalization or localization.