SU(2)xSU(2) Invariant Scattering Matrix of the Hubbard Model

TL;DR

This paper derives the exact scattering matrix for elementary excitations in the 1D half-filled Hubbard model, revealing its $SU(2) imes SU(2)$ symmetry and the relation between repulsive and attractive cases.

Contribution

It provides the explicit form of the $SU(2) imes SU(2)$ invariant scattering matrix, solving the Yang-Baxter equation for the model's excitations.

Findings

Exact two-particle scattering matrix determined

Reflects the $SO(4)$ symmetry of the Hubbard model

Shows relation between repulsive and attractive cases

Abstract

We consider the one-dimensional half-filled Hubbard model. We show that the excitation spectrum is given by the scattering states of four elementary excitations, which form the fundamental representation of $SU(2)\times SU(2)$. We determine the exact two-particle Scattering matrix, which a solution of the Yang-Baxter equation and reflects the $SO(4)$ symmetry of the model. The results for repulsive and attractive Hubbard model are related by an interchange of spin and charge degrees of freedom.