Degenerate approach to the mean field Bose- Hubbard Hamiltonian
  A degenerate variant of mean field perturbation theory for the on-site Bose-Hubbard Hamiltonian is presented. We split the perturbation into two terms and perform exact diagonalization in the two-dimensional subspace corresponding to the degenerate states. The final relations for the second order ground state energy and first order wave function do not contain singularities at integer values of the chemical potentials. The resulting equation for the phase boundary between superfluid and Mott states coincides with the prediction based on the conventional mean field perturbation approach. 
A.M. Belemuk and V.N. Ryzhov
cond-mat.quant-gas