Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 2 (2006), 073, 11 pages      nlin.SI/0611008      https://doi.org/10.3842/SIGMA.2006.073
Contribution to the Proceedings of the Coimbra Workshop on Geometric Aspects of Integrable Systems

Quasi-Exactly Solvable N-Body Spin Hamiltonians with Short-Range Interaction Potentials

A. Enciso, F. Finkel, A. González-López and M.A. Rodríguez
Depto. Física Teórica II, Universidad Complutense, 28040 Madrid, Spain

Received September 15, 2006, in final form October 23, 2006; Published online November 03, 2006

Abstract
We review some recent results on quasi-exactly solvable spin models presenting near-neighbors interactions. These systems can be understood as cyclic generalizations of the usual Calogero-Sutherland models. A nontrivial modification of the exchange operator formalism is used to obtain several infinite families of eigenfunctions of these models in closed form.

Key words: Calogero-Sutherland models; exchange operators; quasi-exact solvability.

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