Consistent low-energy reduction of the three-band model for copper oxides with O-O hopping to the effective<i>t</i>-<i>J</i>model

Abstract

A full three-band model for the ${\mathrm{CuO}}_{2}$ plane with inclusion of all essential interactions---Cu-O and O-O hopping, repulsion at the copper and oxygen and between them---is considered. A general procedure of the low-energy reduction of the primary Hamiltonian to the Hamiltonian of the generalized t-t'-J model is developed. An important role of the direct O-O hopping is discussed. Parameters of the effective low-energy model (the hopping integral, the band position, and the superexchange constant J) are calculated. An analysis of the obtained data shows that the experimental value of J fixes the charge-transfer energy \ensuremath{\Delta}=(${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}$-${\mathrm{\ensuremath{\epsilon}}}_{\mathit{d}}$) in a narrow region of energies.