Critical behavior near the many-body localization transition in driven open systems

TL;DR

This paper investigates the many-body localization transition in open, driven quantum systems coupled to non-thermal baths, revealing critical behavior and proposing a scalable numerical method using matrix-product operators.

Contribution

It introduces a novel approach to study the MBL transition in open systems by tuning bath coupling strength, and proposes a scalable numerical scheme with matrix-product operators.

Findings

Detection of divergence of dynamical exponent due to Griffiths effects

Identification of critical disorder strength for MBL transition

Proposal of a scalable numerical method using Lindblad equation

Abstract

Coupling a many-body localized system to a thermal bath breaks local conservation laws and washes out signatures of localization. When the bath is non-thermal or when the system is also weakly driven, local conserved quantities acquire a highly non-thermal stationary value. We demonstrate how this property can be used to study the many-body localization phase transition in weakly open systems. Here, the strength of the coupling to the non-thermal baths plays a similar role as a finite temperature in a $T=0$ quantum phase transition. By tuning this parameter, we can detect key features of the MBL transition: the divergence of the dynamical exponent due to Griffiths effects in one dimension and the critical disorder strength. We apply these ideas to study the MBL critical point numerically. The possibility to observe critical signatures of the MBL transition in an open system allows for new numerical approaches that overcome the limitations of exact diagonalization studies. Here we propose a scalable numerical scheme to study the MBL critical point using matrix-product operator solution to the Lindblad equation.