Superfluid-insulator transition in weakly interacting disordered Bose gases: a kernel polynomial approach

TL;DR

This paper introduces an efficient kernel polynomial method to analyze coherence and phase transitions in disordered weakly interacting Bose gases across different dimensions, advancing understanding of superfluid-insulator transitions.

Contribution

It presents a novel iterative scheme based on the kernel polynomial method for computing the one-body density matrix in disordered Bose gases within Bogoliubov theory.

Findings

Recovered the superfluid-Bose glass phase boundary in 1D consistent with previous spectral methods.

Studied disorder-induced condensate depletion in 2D Bose gases.

Paved the way for analyzing superfluid-insulator transitions in higher dimensions.

Abstract

An iterative scheme based on the kernel polynomial method is devised for the efficient computation of the one-body density matrix of weakly interacting Bose gases within Bogoliubov theory. This scheme is used to analyze the coherence properties of disordered bosons in one and two dimensions. In the one-dimensional geometry, we examine the quantum phase transition between superfluid and Bose glass at weak interactions, and we recover the scaling of the phase boundary that was characterized using a direct spectral approach by Fontanesi et al. [Phys. Rev. A 81, 053603 (2010)]. The kernel polynomial scheme is also used to study the disorder-induced condensate depletion in the two-dimensional geometry. Our approach paves the way for an analysis of coherence properties of Bose gases across the superfluid-insulator transition in two and three dimensions.