Purification and many-body localization in cold atomic gases

TL;DR

This paper proposes an experimental setup using cold atomic gases to observe many-body localization, demonstrating key signatures like occupation imbalance, entanglement growth, and level statistics through advanced numerical simulations.

Contribution

It introduces a method to detect many-body localization in cold atoms via binary disorder and non-equilibrium dynamics, with exact disorder averaging using a purification approach.

Findings

Occupation imbalance reveals localization signatures.

Logarithmic entanglement growth confirms MBL phase.

Poissonian level statistics support localization evidence.

Abstract

We propose to observe many-body localization in cold atomic gases by realizing a Bose-Hubbard chain with binary disorder and studying its non-equilibrium dynamics. In particular, we show that measuring the difference in occupation between even and odd sites, starting from a prepared density-wave state, provides clear signatures of localization. As hallmarks of the many-body localized phase we confirm, furthermore, a logarithmic increase of the entanglement entropy in time and Poissonian level statistics. Our numerical density-matrix renormalization group calculations for infinite system size are based on a purification approach; this allows us to perform the disorder average exactly, thus producing data without any statistical noise and with maximal simulation times of up to a factor 10 longer than in the clean case.