03-314 J.-B. Bru and T. C. Dorlas
Exact solution of the infinite-range-hopping Bose-Hubbard model (1680K, Postcript) Jun 30, 03
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Abstract. The thermodynamic behavior of the Bose-Hubbard model is solved for any temperature and any chemical potential. It is found that there is a range of critical coupling strengths $\lambda_{c1} < \lambda_{c2} < \lambda_{c3} < \dots$ in this model. For coupling strengths between $\lambda_{c,k}$ and $% \lambda_{c,k+1}$, Bose-Einstein condensation is suppressed at densities near the integer values $\rho = 1, \dots, k$ with an energy gap. This is known as a Mott insulator phase and was previously shown only for zero temperature. In the context of ultra-cold atoms, this phenomenon was experimentally observed in 2002 \cite{BoseCondInsulator1} but, in the Bose-Hubbard model, it manifests itself also in the pressure-volume diagram at high pressures. It is suggested that this phenomenon persists for finite-range hopping and might also be experimentally observable.

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