Phase transition as a function of orbital degeneracy in a generalized Hubbard model

We study a two-band Hubbard model with one copper and one oxygen orbital in each cell. These orbitals are hybridized within a cell, and different cells are coupled via oxygen-oxygen hopping. The Hubbard interaction is set equal to zero on oxygen and infinity on copper. We show that, for sufficiently small oxygen bandwidth, the system is insulating at half filling whatever the value of Δ (the energy difference between the oxygen and copper orbitals). This contradicts the prediction of the slave-boson mean-field theory that there is a metal-insulator transition at a fixed value of Δ=${\mathrm{\Delta }}_{\mathit{c}}$, independent of the oxygen bandwidth in the narrow-bandwidth limit. In order to understand this discrepancy, we study a generalized model in which the degeneracy of the copper orbitals in a given cell is N. Slave-boson mean-field theory is exact in the N→∞ limit, indicating that there is a phase transition at some value of N. This question is studied further by a combination of 1/N expansion around the N=∞ point, and numerical diagonalization up to N=16. It is found that for the physical case of N=2, the results obtained from the large-N theory are qualitatively and quantitatively reliable only for Δ>${\mathrm{\Delta }}_{\mathit{c}}$, i.e., when there is no Bose condensation in the N→∞ limit.