J.-B. Bru and T. C. Dorlas
Exact solution of the infinite-range-hopping Bose-Hubbard model
(1680K, Postcript)
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.