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

Abstract

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.

arXiv commentRevTeX, 31 pages, no figures; important additional content

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Cited by in corpus (4)

• Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions
• A novel quasi-exactly solvable spin chain with nearest-neighbors interactions
• Quasi-Exactly Solvable N-Body Spin Hamiltonians with Short-Range Interaction Potentials
• Jastrow-like ground states for quantum many-body potentials with near-neighbors interactions