2D EXTENDED HUBBARD-MODEL - A SUPERSYMMETRIC CHAIN-CLUSTER APPROACH

A two-step linearization scheme is proposed to approach the 2D extended Hubbard model: (i) by a chain-cluster linearization, the model is first mapped onto a self-consistent 1D problem for a modified extended Hubbard model; (ii) a further linearization is then performed in the proximity of the U(2/2)-supersymmetric model introduced by Essler, Korepin and Schoutens (EKS). The resulting Hamiltonian is shown to be equivalent to a 1D EKS Hamiltonian whose coefficients have to be determined self-consistently. The self-consistency equations can be obtained thanks to the exact solvability of the EKS model.