Finite lattice Bethe ansatz systems and the Heun equation

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.

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

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Cited by in corpus (13)

• T-systems and Y-systems in integrable systems
• Heun Functions and Some of Their Applications in Physics
• The q-deformed analogue of the Onsager algebra: Beyond the Bethe ansatz approach
• Pseudo-differential equations, and the Bethe Ansatz for the classical Lie algebras
• Eight-vertex model and non-stationary Lame equation
• On polynomial solutions of Heun equation
• The eight-vertex model and lattice supersymmetry
• Geometric aspects of the ODE/IM correspondence
• Orthogonal Polynomials, Asymptotics and Heun Equations
• Complex Periodic Potentials with a Finite Number of Band Gaps
• Auxiliary matrices for the six-vertex model and the algebraic Bethe ansatz
• Elementary functions in Thermodynamic Bethe Ansatz
• On Baxter's Q operator of the higher spin XXZ chain at the Razumov-Stroganov point