Bose-Einstein condensation in an exactly solvable model of strongly interacting bosons

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. (author)