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We present results of path-integral Monte Carlo simulations of bosons on a two-dimensional square lattice in a random potential of average strength V and with on-site repulsion U. We find that the superfluid density ₒ is enhanced by increasing V and U in certain regions of parameter space. By combining the results of ₒ, with the behavior of the density-density correlation function on lattices of size up to 1010, we study the superfluid--to--Mott-insulator transition and the transition from a superfluid to a disorder-localized (``Bose glass'') phase.
Krauth et al. (1991) studied this question.