We study a gas of repulsively interacting bosons in an optical lattice and explore the physics beyond the lowest-band Hubbard model. Utilizing a generalized Gutzwiller ansatz, we find how the lowest-band physics is modified by the inclusion of the first excited bands. In contrast to the predictions of the lowest-band Bose-Hubbard model based on mean-field theories, a re-entrant behavior of superfluidity is envisaged as well as decreasing width of the Mott lobes at strong coupling.
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Larson et al. (2009) studied this question.
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