Solvable scalar and spin models with near-neighbors interactions



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Enciso, A. and Finkel Morgenstern, Federico and González López, Artemio and Rodríguez González, Miguel Ángel (2005) Solvable scalar and spin models with near-neighbors interactions. Physics letters B, 605 (1-feb). pp. 214-222. ISSN 0370-2693

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We construct new solvable rational and trigonometric spin models with near-neighbors interactions by an extension of the Dunkl operator formalism. In the trigonometric case we obtain a finite number of energy levels in the center of mass frame, while the rational models are shown to possess an equally spaced infinite algebraic spectrum. For the trigonometric and one of the rational models, the corresponding eigenfunctions are explicitly computed. We also study the scalar reductions of the models, some of which had already appeared in the literature, and compute their algebraic eigenfunctions in closed form. In the rational cases, for which only partial results were available, we give concise expressions of the eigenfunctions in terms of generalized Laguerre and Jacobi polynomials.

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©2004 Elsevier B.V.
This work was partially supported by the Spanish DGI under grant No. BFM2002-02646. A.E. acknowledges the financial support of the Spanish Ministry of Education through an FPU scholarship

Uncontrolled Keywords:Calogero-sutherland moodel; Many-body problem; One-dimension; Fractional statistics; Integrable systems; Super-calogero; Ground-state; Chain; Operators; Exchange
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:32856
Deposited On:25 Aug 2015 07:46
Last Modified:10 Dec 2018 15:09

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