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 λ c1 < λ c2 < λ c3 < ⋅⋅⋅ in this model. For coupling strengths between λ c,k and λ c,k+1, Bose–Einstein condensation is suppressed at densities near the integer values ρ = 1,...,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(1) 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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Bru, JB., Dorlas, T.C. Exact Solution of the Infinite-Range-Hopping Bose–Hubbard Model. Journal of Statistical Physics 113, 177–196 (2003). https://doi.org/10.1023/A:1025774821712
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DOI: https://doi.org/10.1023/A:1025774821712