Algebraic properties of the bethe ansatz for an spl(2,1)-supersymmetric t-j model

Abstract

We investigate the algebraic structure of the supersymmetric t−J model in one dimension. We prove that the Bethe ansatz states are highest-weight vectors of an spl(2,1) superalgebra. By acting with shift operators we construct a complete set of states for this model. In addition we analyse the multiplet structure of the anti-ferromagnetic ground state and some low-lying excitations. It turns out that the ground state is a member of a quartet.