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

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

1994-03-18

arxiv.org/abs/hep-th/9403107v2

J.Phys.A30:1209-1226,1997

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, PlainTEX

Scientific paper

10.1088/0305-4470/30/4/022

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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