Quantum Monte Carlo Simulations of the Kosterlitz-Thouless Transition for Two-Dimensional Disordered Bose-Hubbard Model

In two-dimensional (2D) Bose systems, it is well known that Koterlitz-Thouless (KT) transition occurs. In this report, we perform quantum Monte Carlo simulations to investigate the 2D disordered Bose-Hubbard model. The chemical potential is assumed to depend on the site randomly and its distribution is given by a Gaussian distribution. The KT transition is confirmed from the finite-size analysis of superfluid density and the critical exponent of correlation function. By changing the variance of the Gaussian distribution, we found that the transition temperature decreases as the variance increases. The phase diagram is obtained to show the superfluid and the disordered phases. We try to understand our results by using the concept of “percolation”.