The effective t-J Hamiltonian for the copper oxides

@article{RodrguezNez1993TheET,
  title={The effective t-J Hamiltonian for the copper oxides},
  author={Jos{\'e} Jes{\'u}s Rodr{\'i}guez-N{\'u}{\~n}ez and Hans Peter Beck},
  journal={Journal of Physics: Condensed Matter},
  year={1993},
  volume={5}
}
Starting from the Emery model, which is assumed to describe the copper-oxygen planes, and including direct oxygen hopping matrix elements, tpp, 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 tpd, the hybridization matrix element. The spin-dependent part of the effective Hamiltonian is composed of two contributions: the superexchange interaction, and another one of RKKY type. The effective… 
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