Bethe Ansatz Equations of XXZ Model and q-Sturm-Liouville Problems

Details Bethe Ansatz Equations of XXZ Model and q-Sturm-Liouville Problems Bethe Ansatz Equations of XXZ Model and q-Sturm-Liouville Problems

2004-07-16

arxiv.org/abs/math-ph/0407033v1

Physics

Mathematical Physics

Latex 23 pages

Scientific paper

In this article we have discovered a close relationship between the (algebraic) Bethe Ansatz equations of the spin $s$ XXZ model of a finite size and the $q$-Sturm-Liouville problem. We have demonstrated that solutions of the Bethe Ansatz equations give rise to the polynomial solutions of a second order $q$-difference equation in terms of Askey-Wilson operator. The more general form of Bethe Ansatz equations and the mathematical problems relevant to the physics of XXZ model are discussed. Furthermore, the similar correspondence between Bethe Ansatz equations of XXX model and the Sturm-Liouville type difference equation in terms of Wilson operator has also been found.

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