Exchange operator formalism for N-body spin models with near-neighbors interactions

Details Exchange operator formalism for N-body spin models with near-neighbors interactions Exchange operator formalism for N-body spin models with near-neighbors interactions

2006-04-27

arxiv.org/abs/nlin/0604073v2

J.Phys.A40:1857-1884,2007

Nonlinear Sciences

Exactly Solvable and Integrable Systems

RevTeX, 31 pages, no figures; important additional content

Scientific paper

10.1088/1751-8113/40/8/012

We present a detailed analysis of the spin models with near-neighbors interactions constructed in our previous paper [Phys. Lett. B 605 (2005) 214] by a suitable generalization of the exchange operator formalism. We provide a complete description of a certain flag of finite-dimensional spaces of spin functions preserved by the Hamiltonian of each model. By explicitly diagonalizing the Hamiltonian in the latter spaces, we compute several infinite families of eigenfunctions of the above models in closed form in terms of generalized Laguerre and Jacobi polynomials.

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