Finite lattice Bethe ansatz systems and the Heun equation

Details Finite lattice Bethe ansatz systems and the Heun equation Finite lattice Bethe ansatz systems and the Heun equation

2003-08-07

arxiv.org/abs/hep-th/0308053v2

J.Phys.A37:2047-2062,2004

Physics

High Energy Physics

High Energy Physics - Theory

18+1 pages, 4 figures, typo corrected, references added

Scientific paper

10.1088/0305-4470/37/6/006

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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