DILUTE SYSTEM OF HARD-CORE BOSONS - A SOLUBLE LIMIT

A model for bosons with N degenerate energy levels per site and a hard -core interaction of bosons at the same level is introduced. The limit N --> infinity can be solved exactly in terms of a saddle point integ ration. The zero temperature limit is investigated where the quantum f luctuations drive a transition from an insulating to a superfluid phas e. The results of the calculations agree with those of the mean-field theory for weakly interacting bosons only near the phase transition.