Numerical Study of Disordered Noninteracting Chains Coupled to a Local Lindblad Bath

TL;DR

This study numerically investigates how disordered noninteracting chains coupled to local Lindblad baths exhibit finite-size effects, revealing complex relaxation behaviors that inform understanding of many-body localization phenomena.

Contribution

It provides the first detailed numerical analysis of boundary-coupled disordered noninteracting chains, highlighting finite-size effects on the Lindbladian gap and relaxation dynamics.

Findings

Strong finite-size effects in Lindbladian gap observed

Non-monotonic behavior of relaxation with system size

Insights into localization stability in open quantum systems

Abstract

Disorder can prevent many-body quantum systems from reaching thermal equilibrium, leading to a many-body localized phase. Recent works suggest that nonperturbative effects caused by rare regions of low disorder may destabilize the localized phase. However, numerical simulations of interacting systems are generically possible only for small system sizes, where finite-size effects might dominate. Here we perform a numerical investigation of noninteracting disordered spin chains coupled to a local Lindblad bath at the boundary. Our results reveal strong finite-size effects in the Lindbladian gap in both bath-coupled Anderson and Aubry-Andr\'e-Harper models, leading to a non-monotonic behavior with the system size. We discuss the relaxation properties of a simple toy model coupled to local Lindblad baths, connecting its features to those of noninteracting localized chains. We comment on the implications of our findings for many-body systems.