On the Sutherland Spin Model of B_N Type and its Associated Spin Chain

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".

arXiv comment17 pages, typeset with revtex4 and amsmath. Minor changes only. To appear in Commun. Math. Phys

References in corpus (21)

• Exchange Operator Formalism for Integrable Systems of Particles
• Yang-Baxter equation in spin chains with long range interactions
• The Calogero-Sutherland Model and Generalized Classical Polynomials
• Exact operator solution of the Calogero-Sutherland model
• Lattice Integrable Systems of Haldane-Shastry Type
• Hamiltonian systems of Calogero type and two dimensional Yang-Mills theory
• On Models with Inverse-Square Exchange
• Calogero-Moser Systems in SU(N) Seiberg-Witten Theory
• Solution of Some Integrable One-Dimensional Quantum Systems
• Waves and Solitons in the Continuum Limit of the Calogero-Sutherland Model
• Spectrum of a spin chain with inverse square exchange
• Invariants of the Haldane-Shastry $SU(N)$ Chain
• Exact Solution of Long-Range Interacting Spin Chains with Boundaries
• Bispectral KP Solutions and Linearization of Calogero-Moser Particle Systems
• A_N-type Dunkl operators and new spin Calogero-Sutherland models
• Integrable $1/r^2$ Spin Chain with Reflecting End
• New spin Calogero-Sutherland models related to B_N-type Dunkl operators
• Generalized Calogero models through reductions by discrete symmetries
• Loop groups, anyons and the Calogero-Sutherland model
• Random Matrix Model and the Calogero-Sutherland Model: A Novel Current-Density Mapping
• Spin dependent extension of Calogero-Sutherland model through anyon like representations of permutation operators

Cited by in corpus (16)

• Haldane-Shastry spin chains of BC_N type
• Open Spin Chains in Super Yang-Mills at Higher Loops: Some Potential Problems with Integrability
• On the level density of spin chains of Haldane--Shastry type
• Inozemtsev's hyperbolic spin model and its related spin chain
• Quantum Integrable Systems from Conformal Blocks
• sl(M+1) Construction of Quasi-solvable Quantum M-body Systems
• The spin Sutherland model of D_N type and its associated spin chain
• Integrable N-particle Hamiltonians with Yangian or Reflection Algebra Symmetry
• The exactly solvable spin Sutherland model of B_N type and its related spin chain
• Twisted spin Sutherland models from quantum Hamiltonian reduction
• Exchange operator formalism for N-body spin models with near-neighbors interactions
• Partition functions of Polychronakos like spin chains associated with polarized spin reversal operators
• Sutherland Models for Complex Reflection Groups
• The open Haldane-Shastry chain: thermodynamics and criticality
• Supersymmetric analogue of BC_N type rational integrable models with polarized spin reversal operators
• A Haldane-Shastry spin chain of BC_N type in a constant magnetic field