Finite lattice Bethe ansatz systems and the Heun equation

by Tateo, Roberto

Abstract

We study the P\"oschl-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 a interesting interpretation in terms of finite lattice spin (L-2)/2 XXZ quantum chain with Delta=cos(pi/L), or Delta=-cos(pi/L). This result generalises the findings of Fridkin, Stroganov and Zagier. (Based on hep-th/0308053 [Joint work with Patrick Dorey and Junji Suzuki])