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

摘要

We investigate the Bose glass phase and the insulator-to-superfluid transition 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 found to have a 1/chi(2) tail and the imaginary time Green's function decays algebraically C(tau) similar to tau(-1), giving rise to a divergent global susceptibility. By considering the participation ratio it is shown 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 intervening Bose glass phase for weak disorder. For this transition Re obtain 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 tip of the Mott-lobes and that here the inequality nu greater than or equal to 2/d is violated. [References: 39]