From Bose glass to many-body localization in a one-dimensional disordered Bose gas

TL;DR

This paper explores the finite-temperature phase diagram of a disordered one-dimensional Bose gas, identifying regimes of glassy behavior, a possible localized phase below a critical temperature, and the transition to a normal fluid.

Contribution

It introduces two scenarios for the phase diagram using bosonization and RG, proposing a localized phase below a critical temperature with characteristics similar to many-body localization.

Findings

Disorder effects diminish at high temperatures, leading to a normal fluid.

A localized phase may exist below a critical temperature T_c.

Glassy properties are observed on intermediate scales in certain regimes.

Abstract

We determine the finite-temperature phase diagram of a one-dimensional disordered Bose gas using bosonization and the nonperturbative functional renormalization group (RG). We discuss two different scenarios, based on distinct truncations of the effective action. In the first scenario, the Bose glass is destabilized at any finite temperature, giving rise to a normal fluid. Nevertheless, one can distinguish a low-temperature glassy regime, where disorder plays an important role on intermediate length and time scales, from a high-temperature regime, where disorder becomes irrelevant. In the second scenario, below a temperature $T_c$, the RG flow exhibits a singularity at a finite value of the RG momentum scale. We propose that this singularity signals a lack of thermalization and the existence of a localized phase for $T<T_c$. We provide a description of this low-temperature localized phase within a droplet picture and highlight a number of possible similarities with characteristics of many-body localized phases, including non-thermal behavior, avalanche instabilities and many-body resonances, the structure of the many-body spectrum, and slow dynamics in the ergodic phase. The normal fluid above $T_c$, and below a crossover temperature $T_g$, exhibits glassy properties on intermediate scales.