Fermionic R-Operator and Integrability of the One-Dimensional Hubbard Model

TL;DR

This paper introduces a new fermionic R-operator framework based on novel Yang-Baxter equations, providing a new proof of the integrability of the 1D Hubbard model and insights into its SO(4) symmetry.

Contribution

It develops a fermionic R-operator using new YBE and DYBE relations, offering a novel proof of the Hubbard model's integrability and a new perspective on its symmetry.

Findings

Constructed fermionic R-operator for 1D Hubbard model

Provided a new proof of integrability for the Hubbard model

Discussed a new approach to SO(4) symmetry

Abstract

We propose a new type of the Yang-Baxter equation (YBE) and the decorated Yang-Baxter equation (DYBE). Those relations for the fermionic R-operator were introduced recently as a tool to treat the integrability of the fermion models. Using the YBE and the DYBE for the XX fermion model, we construct the fermionic R-operator for the one-dimensional (1D) Hubbard model. It gives another proof of the integrability of the 1D Hubbard model. Furthermore a new approach to the SO(4) symmetry of the 1D Hubbard model is discussed.