Perturbation Expansion of the Linear Hubbard Model

Abstract

A linked-diagram perturbation expansion of the linear half-filled-band Hubbard model is developed and carried out through seventh order. The zero-order Hamiltonian is taken to be the intrasite Coulomb repulsion terms, and the perturbation is taken to be the intersite interaction. The degenerate perturbation theory applied here results in an effective Hamiltonian defined on a simple spin space, and is found to consist of terms involving nearest-neighbor, next-nearest-neighbor, and biquadratic spin operators.