Accessing many-body localized states through the Generalized Gibbs Ensemble

TL;DR

This paper introduces a quantum Monte Carlo method to study large many-body localized systems by constructing high-quality local integrals of motion, enabling exploration of their thermodynamic properties and suggesting the existence of a full MBL phase in 2D.

Contribution

The authors develop a heuristic approach to incorporate local integrals of motion into simulations, allowing for the study of MBL systems beyond one dimension.

Findings

Method effectively captures MBL characteristics without averaging out key features.

Supports the hypothesis of a full many-body localized phase in two dimensions.

Enables thermodynamic analysis of large MBL systems using quantum Monte Carlo.

Abstract

We show how the thermodynamic properties of large many-body localized systems can be studied using quantum Monte Carlo simulations. To this end we devise a heuristic way of constructing local integrals of motion of very high quality, which are added to the Hamiltonian in conjunction with Lagrange multipliers. The ground state simulation of the shifted Hamiltonian corresponds to a high-energy state of the original Hamiltonian in case of exactly known local integrals of motion. We can show that the inevitable mixing between eigenstates as a consequence of non-perfect integrals of motion is weak enough such that the characteristics of many-body localized systems are not averaged out in our approach, unlike the standard ensembles of statistical mechanics. Our method paves the way to study higher dimensions and indicates that a full many-body localized phase in 2d, where (nearly) all eigenstates are localized, is likely to exist.