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

Abstract

A full three-band model for the 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 $t$-$t^{\prime }$-$J$ 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 $\Delta =({\epsilon }_p-{\epsilon }_d)$ in a narrow region of energies.

32 pp. (LATEX), two figures (PostScript) appended