The algebraic Bethe ansatz for open vertex models

Abstract

We present a unified algebraic Bethe ansatz for open vertex models which are associated with the non-exceptional $A_{2n}^{(2)},A_{2n-1}^{(2)},B_n^{(1)},C_n^{(1)},D_n^{(1)}$ Lie algebras. By the method, we solve these models with the trivial K matrix and find that our results agree with that obtained by analytical Bethe ansatz. We also solve the $B_n^{(1)},C_n^{(1)},D_n^{(1)}$ models with some non-trivial diagonal K-matrices (one free parameter case) by the algebraic Bethe ansatz.

Latex, 35 pages, new content and references are added, minor revisions are made

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• Spectrum of the supersymmetric t-J model with non-diagonal open boundaries
• The spectrum of quantum-group-invariant transfer matrices
• Off-diagonal Bethe Ansatz for the $D_3^{(1)}$ model
• Exact solution of a quantum integrable system associated with the $G_2$ exceptional Lie algebra