Rigorous solution of a Hubbard model extended by nearest-neighbor Coulomb and isotropic exchange interaction on a triangle and tetrahedron

TL;DR

This paper provides a rigorous solution to an extended Hubbard model on a triangle and tetrahedron, correcting previous errors and analyzing the effects of anisotropic and isotropic exchange interactions.

Contribution

It corrects a coding error in earlier work and offers a detailed solution of the extended Hubbard model with anisotropic exchange interactions.

Findings

Results for J=0 remain unchanged from previous work.

Extended Hubbard model with anisotropic exchange is related to the XXZ model.

Corrected results for isotropic exchange are presented.

Abstract

In the preprint cond-mat/0701060 we detected a factor two error in the coding of the Heisenberg term of the Hamiltonian. In the result the exchange term used in the paper was that of an anisotropic Heisenberg model with $J_x=J_y=J$ and $J_z=J/2$. Thus all results given for which J=0 was chosen, remain unchanged, whereas all results containing the exchange parameter remain true for the extended Hubbard model with anisotropic exchange. That model is of some interest by itself, due to the relation to the XXZ model. The differing results for isotropic exchange are given here.