Abstract
An exact algebraic solution is presented for the spectrum of the Bose-Hubbard model for pure systems in the limit of infinite-range hopping and infinite on-site repulsion. This strongly interacting boson system is shown to exhibit Bose-Einstein condensation into the lowest unperturbed single-particle state, with a transition temperature which, for any density of bosons, is always lower than that in the absence of interactions.
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