Local density of the Bose-glass phase

We study the local density of the Bose-Hubbard model in the presence of on-site disorder near the Bose-glass transition using multifractal, typical medium, and percolation theories. At incommensurate filling our findings support the scenario of percolating superfluid clusters enhancing Anderson localization. Scaling analysis of the superfluid density at the incommensurate filling of rho = 1.1 and on-site interaction U = 80t predicts a superfluid-Bose-glass transition at disorder strength of Delta(c) approximate to 30t. At this filling the local-density distribution becomes more skew with increasing disorder strength. Multifractal analysis suggests a multifractal behavior resembling that of the Anderson localization. In the Bose-glass phase the mode of the local-density distribution approaches an integer value as expected from typical medium theory for the Anderson localization. Percolation analysis points to a phase transition of percolating non-integer filled sites around the same value of disorder. On the other hand, the behavior at commensurate filling is rather different. Close to the tip of the Mott lobe (rho = 1, U = 22t) we find a Mott-insulator-Bose-glass transition at disorder strength of Delta(c) approximate to 16t. An analysis of the local-density distribution shows Gaussian-like behavior for a wide range of disorders above and below the transition.