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

Abstract

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.