Scattering matrix and excitation spectrum of the Hubbard model.

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. Pacs: 75.10.Jm , 05.50.q ♭e-mail: [email protected] Address after Sept.1, 1993: Physikalisches Institut der Universität Bonn, Nussallee 12, 53115 Bonn, Germany ♯e-mail: [email protected] Strongly correlated electronic systems are currently under intense study in relation with high-Tc superconductivity. The two-dimensional Hubbard model is in the very center of these investigations. It is believed to share important features with its one-dimensional analog. A very interesting problem is the separation of spin and charge in the Hubbard model in one and two dimensions. In one spatial dimension the Hubbard model can be solved exactly by means of the Bethe Ansatz. The Hubbard hamiltonian is given by the following expression