Mott insulator–superfluid transitions in a two-band model at finite temperature and possible application to supersolidHe4

Abstract

We study the Mott insulator--superfluid transition in a two-band boson Hubbard model, which can be mapped onto a spin-$1∕2$ $XY$ model with spins coupled to an additional Ising degree of freedom. By using a modified mean field theory that includes the effects of phase fluctuations, we show that the transition is first order at both zero and finite temperatures. On the Mott insulator side, there may be reentrance in phase transition. These features are consequences of the underlying transition between competing defect poor and defect rich phases. The possible relevance of the model and our results to supersolid $^{4}\mathrm{He}$ and cold bosonic atoms in optical lattices are discussed.