The Exact Solution of the SU(3) Hubbard Model

TL;DR

This paper derives the exact Bethe ansatz solution for the one-dimensional SU(3) Hubbard model, providing a comprehensive analytical framework for understanding its ground state and spectral properties.

Contribution

It systematically derives the Bethe ansatz equations and eigenstates for the SU(3) Hubbard model using quantum inverse scattering, a novel approach for this system.

Findings

Exact Bethe ansatz equations obtained

Eigenvalues and eigenvectors explicitly derived

Analytic ground state solution provided

Abstract

The Bethe ansatz equations of the 1-D SU(3) Hubbard model are systematically derived by diagonalizing the inhomogeneous transfer matrix of the XXX model. We first derive the scattering matrix of the SU(3) Hubbard model through the coordinate Bethe ansatz method. Then, with the help quantum inverse scattering method we solve the nested transfer matrix and give the eigenvalues, the eigenvectors and the Bethe ansatz equations. Finally, we obtain the exactly analytic solution for the ground state.