STRONG-COUPLING EXPANSIONS FOR THE PURE AND DISORDERED BOSE-HUBBARD MODEL

A strong-coupling expansion for the phase boundary of the (incompressi ble) Mott insulator is presented for the Bose-Hubbard model. Both the pure case and the disordered case are examined. Extrapolations of the series expansions provide results that are as accurate as the Monte Ca rlo simulations and agree with the exact solutions. The shape differen ce between Kosterlitz-Thouless critical behavior in one-dimension and power-law singularities in higher dimensions arises naturally in this strong-coupling expansion. Bounded disorder distributions produce a '' first-order'' kink to the Mott phase boundary in the thermodynamic lim it because of the presence of Lifshitz's rare regions.