Superfluid-Mott-insulator phase transition of bosons in an optical lattice

The Bose-Hubbard model describing interacting bosons in an optical lattice is reduced to a simple spin-1 XY model with single-ion anisotropy in the vicinity of the Mott phase. We propose a mean-field theory based on a constraint SU(3) pseudo-boson representation on the effective model to study the properties of the superfluid-Mott-insulator phase transition. By calculating the elementary excitation spectra and the average particle number fluctuation in the Brillouin zone center, we find that the energy gaps vanish continuously around (J(XY)/J(z))(c) approximate to 0.175 and (J(XY)/J(z))(c) approximate to 0.094 for 2D and 3D cubic lattices respectively, where the superfluid order parameters come up from zero and the Mott insulator state changes into a superfluid state.