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Abstract
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 → ∞ can be solved exactly in terms of a saddle point integration. The zero temperature limit is investigated where the quantum fluctuations drive a transition from an insulating to a superfluid phase. The results of the calculations agree with those of the mean-field theory for weakly interacting bosons only near the phase transition.
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