Mean field theory for the N-orbital Hubbard model beyond the Hubbard I approximation

Using a diagram technique for the Hubbard operators we have constructed a mean field approximation for the N-orbital Hubbard model with diagonal and non-diagonal hopping. The self-consistent renormalization of the lower and upper Hubbard subband centers, which is absent in the Hubbard I approximation, is of the order of Nt(1)(2)z/U, where t(1) is the diagonal hopping matrix element and z is the coordination number. This leads to different renormalizations of the Hubbard intra-atomic interaction U in the localized (Mott) phase with magnetic moment and the delocalized Paramagnetic phase. The second model shows that the main role in the Mott localization-delocalization phenomenon is played by non-diagonal hopping, giving rise to two wide Hubbard subbands and 2(N-1) narrow ones.