A note on the boundary spin $s$ XXZ chain

Abstract

The open spin $s$ XXZ model with non-diagonal boundaries is considered. Within the algebraic Bethe ansatz framework and in the spirit of earlier works we derive suitable reference states. The derivation of the reference state is the crucial point in this investigation, and it involves the solution of sets of difference equations. For the spin $s$ representation, expressed in terms of difference operators, the pseudo-vacuum is identified in terms of $q$-hypergeometric series. Having specified such states we then build the Bethe states and also identify the spectrum of the model for generic values of the anisotropy parameter $q$.

12 pages, Latex

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Cited by in corpus (14)

• Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions
• Complete Bethe Ansatz solution of the open spin-s XXZ chain with general integrable boundary terms
• Bethe ansatz of the open spin-s XXZ chain with nondiagonal boundary terms
• Algebraic Bethe ansatz for the six vertex model with upper triangular $K$-matrices
• Diagonalization of the Heun-Askey-Wilson operator, Leonard pairs and the algebraic Bethe ansatz
• Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin model
• Generalized T-Q relations and the open spin-s XXZ chain with nondiagonal boundary terms
• Nested algebraic Bethe ansatz for open GL(N) spin chains with projected K-matrices
• Algebraic Bethe ansatz for the trigonometric sl(2) Gaudin model with triangular boundary
• Generic boundary scattering in the open XXZ chain
• Algebraic Bethe ansatz for 19-vertex models with upper triangular K-matrices
• BPS Monopoles and Open Spin Chains
• Non-diagonal reflection for the non-critical XXZ model
• The spectrum of an open vertex model based on the U_q[SU(2)] at roots of unity