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On the second reference state and complete eigenstates of the open XXZ chain

Wen‐Li Yang, Yao-Zhong Zhang

Published Mar 26, 2007• 53 citations
OpenAlex

Abstract

The second reference state of the open XXZ spin chain with non-diagonal boundary terms is studied. The associated Bethe states exactly yield the second set of eigenvalues proposed recently by functional Bethe Ansatz. In the quasi-classical limit, two sets of Bethe states give the complete eigenstates of the associated Gaudin model.

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Addendum to the paper J. Phys. A36 (2003) 1391-1401: \nA Bethe Ansatz solution of the open spin-1/2 XXZ quantum spin chain with nondiagonal boundary terms has recently been proposed. Using a numerical procedure developed by McCoy et al, we find significant evidence that this solution can yield the complete set of eigenvalues for generic values of the bulk and boundary parameters satisfying one linear relation. Moreover, our results suggest that this solution is practical for investigating the ground state of this model in the thermodynamic limit.
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Based on the inhomogeneous T−Q relation constructed via the off-diagonal Bethe Ansatz, the Bethe-type eigenstates of the XXZ spin-12 chain with arbitrary boundary fields are constructed. It is found that by employing two sets of gauge transformations, proper generators and reference state for constructing Bethe vectors can be obtained respectively. Given an inhomogeneous T−Q relation for an eigenvalue, it is proven that the resulting Bethe state is an eigenstate of the transfer matrix, provided that the parameters of the generators satisfy the associated Bethe Ansatz equations.