Completeness of Bethe's states for generalized XXZ model
Anatol N. Kirillov, Nadejda A. Liskova
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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