THE 2-DIMENSIONAL DISORDERED BOSON HUBBARD-MODEL - EVIDENCE FOR A DIRECT MOTT-INSULATOR-TO-SUPERFLUID TRANSITION AND LOCALIZATION IN THE BOSE GLASS PHASE

We investigate the Bose glass phase and the insulator-to-superfluid tr ansition in the two-dimensional disordered Boson Hubbard model in the Villain representation via Monte Carlo simulations. In the Bose glass phase the probability distribution of the local susceptibility is foun d to have a 1/chi(2) tail and the imaginary time Green's function deca ys algebraically C(tau) similar to tau(-1), giving rise to a divergent global susceptibility. By considering the participation ratio it is s hown that the excitations in the Bose glass phase are fully localized and a scaling law is established. For commensurate Boson densities we find a direct Mott insulator to superfluid transition without an inter vening Bose glass phase for weak disorder. For this transition Re obta in the critical exponents z = 1, nu = 0.7 +/- 0.1 and eta = 0.1 +/- 0. 1, which agree with those for the classical three-dimensional XY model without disorder. This indicates that disorder is irrelevant at the t ip of the Mott-lobes and that here the inequality nu greater than or e qual to 2/d is violated.