Bethe Ansatz Equations of XXZ Model and q-Sturm-Liouville Problems
Mathematical Physics
2007-05-23 v1 High Energy Physics - Theory
math.MP
Quantum Algebra
Abstract
In this article we have discovered a close relationship between the (algebraic) Bethe Ansatz equations of the spin XXZ model of a finite size and the -Sturm-Liouville problem. We have demonstrated that solutions of the Bethe Ansatz equations give rise to the polynomial solutions of a second order -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.
Keywords
Cite
@article{arxiv.math-ph/0407033,
title = {Bethe Ansatz Equations of XXZ Model and q-Sturm-Liouville Problems},
author = {M. E. H. Ismail and S. S. Lin and S. S. Roan},
journal= {arXiv preprint arXiv:math-ph/0407033},
year = {2007}
}
Comments
Latex 23 pages