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

We study the Villain representation of the two-dimensional disordered boson Hubbard model via Monte Carlo simulations. It is shown that the probability distribution of the local susceptibility has a $1/\chi^2$-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 $z=1$, $\nu\sim0.7$ and $\eta\sim0.1$, which are reminiscent of the pure three-dimensional classical XY model.