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

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 $A$.

20 pages, PlainTEX

References in corpus (2)

• Continued Fractions and Fermionic Representations for Characters of M(p,p') minimal models
• Construction of Modular Branching Functions from Bethe's Equations in the 3-State Potts Chain

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