Symmetries of Strongly Correlated Electrons

Abstract

Strongly correlated electronic systems are believed to be of great importance in relation with high-T _c superconductivity. In the very center of attention are the two-dimensional Hubbard and t-J models. It is a very interesting fact that both these models are exactly solvable by Bethe Ansatz in one spatial dimension (the t-J model only at the supersymmetric point J = ±2t). There are indications that the two-dimensional models share important features with their one-dimensional analogs^[1]. One of the many puzzling problems of strongly correlated electronic systems in one and two dimensions is the question of separation of spin and charge degrees of freedom^[2]. In this talk we discuss the importance of symmetries for systems of correlated electrons. We show that both the excitation spectrum over the half-filled ground state and exact Scattering matrix of the Hubbard model are determined by the SO(4) symmetry of the Hubbard hamiltonian. We find that quasiparticles separate into spinless charge-carriers and chargeless spin-carriers, which very nicely and precisely reflets the spin- and charge separation at half filling.