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

TL;DR

This paper develops a consistent method to reduce a comprehensive three-band model of copper oxides, including O-O hopping, to an effective t-J model, providing insights into parameter determination and the role of direct oxygen-oxygen hopping.

Contribution

It introduces a general procedure for low-energy reduction of the three-band Hamiltonian to a generalized t-J model, emphasizing the significance of O-O hopping and calculating key parameters.

Findings

The effective model parameters are quantitatively determined.

The experimental J value constrains the charge transfer energy Δ.

O-O hopping plays a crucial role in the model reduction.

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 $t$-$t'$-$J$ 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.