Hubbard Models as Fusion Products of Free Fermions

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.