Numerical Study of a Many-Body Localized System Coupled to a Bath

TL;DR

This study investigates how many-body localized systems lose their localization when coupled to a thermal bath, revealing a crossover from localized to thermal behavior and persistent incomplete localization signatures.

Contribution

The paper demonstrates that even weak coupling to a bath can destroy many-body localization, with detailed spectral analysis showing residual localization features.

Findings

Level statistics transition from Poisson to GOE

Eigenstates thermalize with increasing bath coupling

Spectral functions show incomplete localization signatures

Abstract

We use exact diagonalization to study the breakdown of many-body localization in a strongly disordered and interacting system coupled to a thermalizing environment. We show that the many-body level statistics cross over from Poisson to GOE, and the localized eigenstates thermalize, with the crossover coupling decreasing with the size of the bath in a manner consistent with the hypothesis that an infinitesimally small coupling to a thermodynamic bath should destroy localization of the eigenstates. However, signatures of incomplete localization survive in spectral functions of local operators even when the coupling to the environment is non-zero. These include a discrete spectrum and a gap at zero frequency. Both features are washed out by line broadening as one increases the coupling to the bath.