Green's function approach to the Bose-Hubbard model with disorder

We present our results of studing the three different ground states of

spinless bosons with short-range interactions submitted to a random

potential using the disordered Bose-Hubbard model. Applying a

field-theoretical method to construct a perturbative expansion to the

single-particle Green's function, we were able to analyze the criteria for

identifying the superfluid, the Mott-insulator, and the Bose-glass phases

at finite temperatures and for small values of the tunneling energy. By

performing a summation of tree-level contributions of the perturbative

approximation we obtained a condition for the long-range correlations

which leads to the phase boundary between superfluid and insulating

phases. Considering the first relevant contribution to the expansion of

the local correlations we obtained a renormalized expression to the

density of states, which unambiguously distinguishes the Mott-insulator

and Bose-glass phases. As a result, we constructed the phase diagram for

two and three dimensions considering bounded on-site disorder.