Bose-glass and Mott-insulator phase in the disordered boson Hubbard model

We study the two-dimensional disordered boson Hubbard model via quantum Monte Carlo simulations. It is shown that the probability distribution of the local susceptibility has a 1/${\mathrm{\chi }}^2$ tail in the Bose-glass phase. This gives rise to a divergence although particles are completely localized here as we prove with the help of the participation ratio. We demonstrate the presence of an incompressible Mott lobe within the Bose-glass phase and show that a direct Mott-insulator-to-superfluid transition happens at the tip of the lobe. Here we find critical exponents z=1, ν∼0.7 and η∼0.1, which agree with those of the pure three-dimensional classical XY model.