Reduction of three-band model for copper oxides to single-band generalized t~-~J model

TL;DR

This paper derives a simplified single-band generalized t-J model from a more complex three-band model for copper oxides, providing an exact solution and validating the reduction through comparison.

Contribution

It introduces a new method to reduce the three-band model to a single-band generalized t-J model and validates this reduction with an exact solution.

Findings

Excellent agreement between the reduced model and the exact solution.

The reduction simplifies the analysis of copper oxides.

The method applies to parameters where the second hole energy is close to the first on oxygen.

Abstract

A three-band model for copper oxides in the region of parameters where the second hole on the copper has energy close to the first hole on the oxygen is considered. The exact solution for one hole on a ferromagnetic background of the ordered copper spins is obtained. A general procedure for transformation of the primary Hamiltonian to the Hamiltonian of singlet and triplet excitations is proposed. Reduction of the singlet-triplet Hamiltonian to the single-band Hamiltonian of the generalized t~-~J model is performed. A comparison of the solution for the generalized t~-~J model on a ferromagnetic background with the exact solution shows a very good agreement.