This article is cited in 2 papers

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

A. Enciso, F. Finkel, A. González-López, M. A. Rodríguez

Depto. Física Teórica II, Universidad Complutense, 28040 Madrid, Spain

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.

Keywords: Calogero–Sutherland models; exchange operators; quasi-exact solvability.

MSC: 81Q05; 35Q40

Received: September 15, 2006; in final form October 23, 2006; Published online November 3, 2006

Language: English

DOI: 10.3842/SIGMA.2006.073

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ArXiv: nlin.SI/0611008