Effective t-J Hamiltonian for the Copper Oxides

TL;DR

This paper derives an effective t-J Hamiltonian for copper oxides starting from the Emery model, incorporating direct oxygen hopping, using a systematic linked cluster expansion up to fourth order.

Contribution

It introduces a novel derivation of the t-J Hamiltonian from the Emery model including oxygen hopping effects, advancing theoretical understanding of copper oxide electronic structure.

Findings

Derived the effective t-J Hamiltonian including oxygen hopping

Extended the derivation to fourth order in hybridization

Provides a more accurate model for copper oxide planes

Abstract

Starting from the Emery model, which is assumed to describe the copper oxygen planes, and including direct oxygen hopping matrix elements, we have been able to derive the effective t-J Hamiltonian for the copper orbitals using the Linked Cluster Expansion Method up to fourth order in the hybridization matrix element.