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 and its quantum critical phenomenon. 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 changing 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 the disordered phases, and estimate the quantum critical point (QCP) and the critical exponent. Our results on the ground state show the existence of the Bose glass phase. Finally, we discuss what the variance of the QCP indicates from the viewpoint of quantum percolation.