World line simulations of the bosonic Hubbard model in the ground state

We discuss Quantum Monte Carlo simulations for the 1 and 2-dimensional bosonic Hubbard models using the world line algorithm. We first discuss the algorithm and our method for measuring the superfluid density, and determine the ground state phase diagram with and without disorder. We then use the phase diagram and further numerical simulations to examine the question of the universal conductivity observed at the superconductor-insulator transition in disordered films. Finally, we demonstrate the presence of a supersolid phase in a which diagonal long-range order (a lattice structure) and a nonzero superfluid density, coexist. We discuss some of the experimental relevance of this exotic phase.