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arXiv · hep-th/9403107

Completeness of Bethe's states for generalized $XXZ$ model

Anatol N. Kirillov·Nadejda A. Liskova
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Abstract

We study the Bethe ansatz equations for a generalized $XXZ$ model on a one-dimensional lattice. Assuming the string conjecture we propose an integer version for vacancy numbers and prove a combinatorial completeness of Bethe's states for a generalized $XXZ$ model. We find an exact form for inverse matrix related with vacancy numbers and compute its determinant. This inverse matrix has a tridiagonal form, generalizing the Cartan matrix of type $A$.

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Anatol N. Kirillov, Nadejda A. Liskova. 1994-03-23. Completeness of Bethe's states for generalized $XXZ$ model. https://doi.org/10.1088/0305-4470%2F30%2F4%2F022

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