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

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.