Bounding the resources for thermalizing many-body localized systems

TL;DR

This paper establishes bounds on the size of external heat baths needed to thermalize many-body localized systems, using resource theory and quantum information tools, and applies these bounds to a disordered Heisenberg chain.

Contribution

It introduces a novel framework using resource theories and the convex split lemma to quantify the robustness of MBL systems against thermalization.

Findings

Derived bounds on bath size for thermalization of MBL systems.

Applied bounds to the disordered Heisenberg chain and numerically analyzed MBL robustness.

Abstract

Understanding under which conditions physical systems thermalize is a long-standing question in many-body physics. While generic quantum systems thermalize, there are known instances where thermalization is hindered, for example in many-body localized (MBL) systems. Here we introduce a class of stochastic collision models coupling a many-body system out of thermal equilibrium to an external heat bath. We derive upper and lower bounds on the size of the bath required to thermalize the system via such models, under certain assumptions on the Hamiltonian. We use these bounds, expressed in terms of the max-relative entropy, to characterize the robustness of MBL systems against externally-induced thermalization. Our bounds are derived within the framework of resource theories using the convex split lemma, a recent tool developed in quantum information. We apply our results to the disordered Heisenberg chain, and numerically study the robustness of its MBL phase in terms of the required bath size.