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Finite lattice Bethe ansatz systems and the Heun equation

Patrick Dorey·Junji Suzuki·Roberto Tateo
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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) (for free-free boundary conditions), or Delta=-cos(pi/L) (for periodic boundary conditions). This result generalises 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.

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Patrick Dorey, Junji Suzuki, Roberto Tateo. 2003-10-17. Finite lattice Bethe ansatz systems and the Heun equation. https://doi.org/10.1088/0305-4470%2F37%2F6%2F006

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