Localization in the Hopping disordered Bose Hubbard model

The zero-temperature superfluid (SF)-Bose glass (BG) transition in the stro ngly correlated (U = infinity) Bose Hubbard model in d dimensions driven by disorder in hopping is studied using a simple analytic technique. The tran sition is identified as the point at which the density of states for local rotations of phase of the superfluid order parameter is enhanced at the low est energies. This identification leads to the values nu = 2/d and z = d/2 for the correlation length and dynamical exponents, respectively by an appr oximation calculation of the low-energy density of states for large d. At t he transition, the singular part of the compressibility kappa vanishes, so kappa is finite.