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 XYmodel with single-ion anisotropy in the vicinity of the Mott phase.We propose a mean-field theory based on a constraintSU(3)pseudo-boson representation on the effective model to study the properties of the superfluid-Mott-insulator phasetransition.By calculating the elementary excitation spectra and the average particle number fluctuation in the Brillouinzone center,we find that the energy gaps vanish continuously around(J/J)≈0.175 and (J/J)≈0.094 for2D and 3D cubic lattices respectively,where the superfluid order parameters come up from zero and the Mott insulatorstate changes into a superfluid state.