A New Supersymmetric and Exactly Solvable Model of Correlated Electrons

TL;DR

This paper introduces a new supersymmetric lattice model for correlated electrons, extending the Hubbard model with exact solvability in one dimension via Bethe ansatz, and characterized by a superalgebra symmetry.

Contribution

It presents a novel supersymmetric lattice model of correlated electrons based on the $gl(2|1)$ superalgebra, differing from previous extended Hubbard models, with exact 1D solutions.

Findings

Model is exactly solvable in 1D by Bethe ansatz.

Contains a free parameter U related to Hubbard interaction.

Features a supersymmetry algebra $gl(2|1)$.

Abstract

A new lattice model is presented for correlated electrons on the unrestricted $4^L$-dimensional electronic Hilbert space $\otimes_{n=1}^L{\bf C}^4$ (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 irreps of $gl(2|1)$. On a one-dimensional lattice, the model is exactly solvable by the Bethe ansatz.