Quantum Simulations of the Superfluid-Insulator Transition for Two-Dimensional, Disordered, Hard-Core Bosons

We introduce two quantum Monte Carlo algorithms and employ them to study the superfluid-insulator transition in a two-dimensional system of hard-core bosons. One of the algorithms is appropriate for zero temperature and is based upon the Green's function Monte Carlo method; the other is an extension of the finite-temperature world-line cluster method. In each case we find that the dynamical exponent is consistent with the theoretical prediction of $z=2\mathrm{}$ by Fisher and co-workers.