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

Abstract

We present a detailed analysis of the spin models with near-neighbours interactions constructed in our previous paper (Enciso et al 2005 Phys. Lett. B 605 214) 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.