On the Sutherland Spin Model of B N Type and Its Associated Spin Chain

2002/02/28 by Federico Finkel, F. Finkel, David Gómez‐Ullate +7 · 1 citation
Chemistry · Mathematics · Physics and Astronomy · #Advanced NMR Techniques and Applications #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #hep-th #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1007/s00220-002-0742-z

published as Commun.Math.Phys. 233 (2003) 191-209 · 17 pages, typeset with revtex4 and amsmath. Minor changes only. To appear in Commun. Math. Phys

arxiv created 2002/11/06 · openalex publication_date 2003/02/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The B_N hyperbolic Sutherland spin model is expressed in terms of a suitable set of commuting Dunkl operators. This fact is exploited to derive a complete family of commuting integrals of motion of the model, thus establishing its integrability. The Dunkl operators are shown to possess a common flag of invariant finite-dimensional linear spaces of smooth scalar functions. This implies that the Hamiltonian of the model preserves a corresponding flag of smooth spin functions. The discrete spectrum of the restriction of the Hamiltonian to this spin flag is explicitly computed by triangularization. The integrability of the hyperbolic Sutherland spin chain of B_N type associated with the dynamical model is proved using Polychronakos's "freezing trick".

Citations

• Exchange operator formalism for integrable systems of particles
• Invariants of the Haldane-Shastry SU(N) chain
• Exact operator solution of the Calogero-Sutherland model
• Generalized Calogero models through reductions by discrete symmetries
• Solution of the One-Dimensional N-Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials
• Differential-difference operators associated to reflection groups

Cited by

• Sutherland models for complex reflection groups