Superfluid to Bose-glass transition in a 1D weakly interacting Bose gas

TL;DR

This paper investigates the superfluid to Bose-glass transition in a one-dimensional weakly interacting Bose gas with correlated disorder, revealing critical behaviors and phase diagram characteristics at zero temperature.

Contribution

It introduces an extended density-phase Bogoliubov approach to analyze phase transition signatures and localization properties in disordered 1D Bose gases.

Findings

Power-law divergence of the density of states at the transition

Localization length exhibits a -1 power-law energy dependence at the boundary

Phase diagram of superfluid-insulator transition for small interactions

Abstract

We study the one-dimensional Bose gas in spatially correlated disorder at zero temperature, using an extended density-phase Bogoliubov method. We analyze in particular the decay of the one-body density matrix and the behaviour of the Bogoliubov excitations across the phase boundary. We observe that the transition to the Bose glass phase is marked by a power-law divergence of the density of states at low energy. A measure of the localization length displays a power-law energy dependence in both regions, with the exponent equal to -1 at the boundary. We draw the phase diagram of the superfluid-insulator transition in the limit of small interaction strength.