Study of Kosterlitz-Thouless transition of Bose systems governed by a random potential using quantum Monte Carlo simulations

TL;DR

This study uses quantum Monte Carlo simulations to explore how randomness affects the Kosterlitz-Thouless transition in a 2D Bose system, revealing phase diagrams, a Bose glass phase, and the impact of disorder on transition temperature.

Contribution

It provides the first detailed phase diagram of the disordered 2D Bose-Hubbard model and identifies the Bose glass phase using quantum Monte Carlo methods.

Findings

Transition temperature decreases with increasing disorder variance.

Existence of Bose glass phase in the disordered system.

Phase diagram showing superfluid and disordered phases.

Abstract

We perform quantum Monte Carlo simulations to study the 2D hard-core Bose-Hubbard model in a random potential. Our motivation is to investigate the effects of randomness on the Kosterlitz--Thouless (KT) transition. The chemical potential is assumed to be random, by site, with a Gaussian distribution. The KT transition is confirmed by a finite-size analysis of the superfluid density and the power-law decay of the correlation function. By varying the variance of the Gaussian distribution, we find that the transition temperature decreases as the variance increases. We obtain the phase diagram showing the superfluid and disordered phases, and estimate the quantum critical point (QCP). Our results on the ground state reveal the existence of the Bose glass phase. Finally, we discuss what the value of the variance at the QCP indicates from the viewpoint of percolation.