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.

Solution of the vertex model with non-diagonal open boundaries

“…By now this procedure has been well explained in the literature, see for instance refs. [14,15], and here we shall restrict ourselves in presenting only the essential steps of the solution. We first note that diagonal boundaries permit us to use as pseudovacuum the usual ferromagnetic state…”

“…The first ones contribute to the eigenvalue Λ(λ) and are obtained by keeping only the first terms of the commutation rules (13)(14)(15) and by requiring that the coefficients F an 1 ...a 1 are eigenstates of an auxiliary double-row operatorT (1) (λ, {λ (1) j }) given bȳ…”

Drinfeld Twists and Algebraic Bethe Ansatz of the Supersymmetrict-JModel

“…With the help of the simple generators, the non-simple generatorsẼ 13 andẼ 31 of gl(2|1) can be obtained by the commutation relations,…”

“…In this Appendix, we recall the nested Bethe ansatz method [12] [13]. The Hamiltonian (II.11) can be exactly diagonalized by using the nested Bethe ansatz method.…”

“…Using the nested algebraic Bethe ansatz method, Essler and Korepin obtained the eigenvalues of the supersymmetric t-J model [12]. The algebraic structure and physical properties of the model were investigated in [13,14,15].…”