Mott-glass phase induced by long-range correlated disorder in a one-dimensional Bose gas

TL;DR

This paper explores how long-range correlated disorder affects the phase diagram of a one-dimensional Bose gas, revealing a transition from Bose glass to Mott glass phases depending on the disorder correlation decay.

Contribution

It introduces a detailed analysis of the phase diagram considering long-range correlations, identifying the conditions for Bose glass and Mott glass phases using nonperturbative and perturbative RG methods.

Findings

Long-range correlations induce a transition from Bose glass to Mott glass.

Critical Luttinger parameter depends on the correlation decay exponent.

Exactly solvable case for perfectly correlated disorder confirms theoretical predictions.

Abstract

We determine the phase diagram of a one-dimensional Bose gas in the presence of disorder with short- and long-range correlations, the latter decaying with distance as $1/|x|^{1+\sigma}$. When $\sigma<0$, the Berezinskii-Kosterlitz-Thouless transition between the superfluid and the localized phase is driven by the long-range correlations and the Luttinger parameter $K$ takes the critical value $K_c(\sigma)=3/2-\sigma/2$. The localized phase is a Bose glass for $\sigma>\sigma_c=3-\pi^2/3\simeq -0.289868$, and a Mott glass -- characterized by a vanishing compressibility and a gapless conductivity -- when $\sigma<\sigma_c$. Our conclusions, based on the nonperturbative functional renormalization group and perturbative renormalization group, are confirmed by the study of the case $\sigma=-1$, corresponding to a perfectly correlated disorder in space, where the model is exactly solvable in the semiclassical limit $K\to 0^+$.