Scattering Matrix and Excitation Spectrum of the Hubbard Model

TL;DR

This paper analyzes the one-dimensional Hubbard model at half filling, revealing how its excitation spectrum and S-matrix are governed by SO(4) symmetry, with exact solutions satisfying Yang-Baxter relations.

Contribution

It provides the exact S-matrix and excitation spectrum for the Hubbard model, highlighting the role of SO(4) symmetry and the relation between repulsive and attractive cases.

Findings

Excitation spectrum consists of four elementary scattering states.

Exact S-matrix satisfies Yang-Baxter relation.

Repulsive and attractive models are related by spin-charge interchange.

Abstract

We consider the one-dimensional Hubbard model at half filling. We show that both excitation spectrum and S-matrix are determined by the SO(4) symmetry of the model. The complete set of excitations is given by the scattering states four elementary excitations, which form the fundamental representation of SO(4). We evaluate the exact S-matrix, which satisfies the Yang-Baxter relation. The results for the repulsive and attractive Hubbard model are related by an interchange of spin and charge degrees of freedom.