Exact Results on a Supersymmetric Extended Hubbard Model

Abstract

The two most promising models of correlated electrons in relation with high-T _c superconductivity are the Hubbard and t-J models. Both are related to the isotropic spin-1/2 Heisenberg antiferromagnet (XXX model): the Hubbard model via the U → ∞limit and the t-J model by tuning the chemical potential to half-filling. In one dimension the Hubbard model, the t-Jmodel at the supersymmetric point J = ±2t, and the Heisenberg model are integrable and can be solved exactly by means of the Bethe Ansatz^[1–4]. These exact solutions first of all provide checks for other methods employed to study two-dimensional models, they give intuition about the effects of strong correlations, and may even be of direct relevance for the two-dimensional models, which are believed to share important features with their one-dimensional analogs^[5]. The XXX model and the supersymmetric t-Jmodel (st-J) have another interesting common feature: they are maximally symmetric in the sense that their hamiltonians are invariant under all global unitary rotations of the bases of their respective Hilbert spaces. Let us consider a lattice of length L with periodic boundary conditions.