Hubbard Models as Fusion Products of Free Fermions

TL;DR

This paper develops algebraic tools for constructing and analyzing integrable Hubbard-like models from free-fermion models, including solutions, symmetries, and diagonalization methods.

Contribution

It introduces a new algebraic framework for free-fermion models, constructs integrable Hubbard-like models, and provides a simplified proof of the decorated Yang-Baxter equation.

Findings

Derived algebra defining free-fermion models.

Constructed new classes of solutions.

Proved integrability of Hubbard-like models.

Abstract

A class of recently introduced su(n) `free-fermion' models has recently been used to construct generalized Hubbard models. I derive an algebra defining the `free-fermion' models and give new classes of solutions. I then introduce a conjugation matrix and give a new and simple proof of the corresponding decorated Yang-Baxter equation. This provides the algebraic tools required to couple in an integrable way two copies of free-fermion models. Complete integrability of the resulting Hubbard-like models is shown by exhibiting their L and R matrices. Local symmetries of the models are discussed. The diagonalization of the free-fermion models is carried out using the algebraic Bethe Ansatz.