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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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