Ginzburg-Landau effective action approach to disordered Bose-Hubbard Model

We study the phase transition from Mott insulator (MI) to Bose glass (BG) of a disordered Bose-Hubbard model within the framework of Ginzburg-Landau effective action approach. By treating MI as unperturbed ground state and performing a systematic expansion with respect to tunneling matrix element, we extend such a field-theoretic method into the disordered lattice Bose systems. To the lowest order, a second order phase transition is confirmed to happen here and the corresponding phase boundary equation coincides with the previous mean-field approximation result. Keeping all the terms second order in hopping parameter, we obtain the beyond mean-field results of MI-BG phase boundary of 2D and 3D disordered Bose-Hubbard models. Our analytic predictions are in agreement with recent semianalytic results.