  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.
