Local Density distribution of disordered Bose-Hubbard Model

We study the local density of the Bose-Hubbard model in the presence of on-site disorder in the canonical ensemble. 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 ρ=1.1 and on-site interaction U=80t predicts a superfluid-Bose glass transition at disorder strength of Δ_c~30t. At this filling, the local density distribution becomes more skew with increasing disorder strength. 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. On the other hand, the behavior at commensurate filling is rather different. Close to the tip of the Mott lobe ρ=1, U=22t we find a Mott insulator-Bose glass transition at disorder strength of Δ_c~16t. An analysis of the local density distribution shows Gaussian like behavior for a wide range of disorders above and below the transition.