arXiv:hep-th/0308053 · Journal of Physics A Mathematical and General

Finite lattice Bethe ansatz systems and the Heun equation

Patrick Dorey, Junji Suzuki, Roberto Tateo

Published Jan 28, 2004• 20 citations

Abstract

We study the Pöschl–Teller equation in complex domain and deduce infinite families of TQ and Bethe ansatz equations, classified by four integers. In all these models the form of T is very simple, while Q can be explicitly written in terms of the Heun function. At particular values there is an interesting interpretation in terms of finite lattice spin- XXZ quantum chain with (for free–free boundary conditions), or (for periodic boundary conditions). This result generalizes the findings of Fridkin, Stroganov and Zagier. We also discuss the continuous (field theory) limit of these systems in view of the so-called ODE/IM correspondence.

DOI: 10.1088/0305-4470/37/6/006

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