New Supersymmetric and Exactly Solvable Model of Correlated Electrons

Abstract

A new lattice model is presented for correlated electrons on the unrestricted ${4}^{L}$-dimensional electronic Hilbert space ${\ensuremath{\bigotimes}}_{n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1}^{L}{\mathbf{C}}^{4}$ (where $L$ is the lattice length). It is a supersymmetric generalization of the Hubbard model, but differs from the extended Hubbard model proposed by Essler, Korepin, and Schoutens. The supersymmetry algebra of the new model is superalgebra gl(2 $|$1). The model contains one symmetry-preserving free real parameter which is the Hubbard interaction parameter $U$, and has its origin here in the one-parameter family of inequivalent typical 4-dimensional irreducible representations of gl(2 $|$1). On a one-dimensional lattice, the model is exactly solvable by the Bethe ansatz.