Mott and Superfluid Transitions in a Strongly Interacting Lattice Boson System

We present numerical simulations on a lattice model of bosons in two dimensions using a path integral quantum Monte Carlo algorithm. At finite temperature we observe the Kosterlitz-Thouless transition and by a finite-size analysis determine the transition temperature. In the limit of zero temperature we find two distinct phases: at a special commensurate density (number of bosons integer multiple of the number of sites), the system is superfluid for small values of the interaction, but the superfluidity vanishes at a critical value of the interaction and the system becomes a Mott insulator. For an incommensurate density, the system remains superfluid at all values of the repulsive interaction between bosons. The superfluid density, however, vanishes as a commensurate density is approached for sufficiently large interaction. We estimate the critical exponents for these transitions.