The su(N) Hubbard model

TL;DR

This paper introduces an integrable su(n) symmetric generalization of the Hubbard model, extending its symmetry and integrability properties from the well-known su(2) case to higher su(n) cases, applicable in any dimension.

Contribution

The paper presents a new integrable model with extended su(n) symmetry, generalizing the Hubbard model beyond su(2) and demonstrating its integrability through L-matrix and transfer matrix methods.

Findings

The model exhibits su(n) symmetry and integrability.

It generalizes the Hubbard Hamiltonian to any dimension.

Complete integrability is established via L-matrix construction.

Abstract

The one-dimensional Hubbard model is known to possess an extended su(2) symmetry and to be integrable. I introduce an integrable model with an extended su(n) symmetry. This model contains the usual su(2) Hubbard model and has a set of features that makes it the natural su(n) generalization of the Hubbard model. Complete integrability is shown by introducing the L-matrix and showing that the transfer matrix commutes with the hamiltonian. While the model is integrable in one dimension, it provides a generalization of the Hubbard hamiltonian in any dimension.