On the Sutherland Spin Model of B_N Type and its Associated Spin Chain
arXiv:hep-th/0202080 · doi:10.1007/s00220-002-0742-z
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".
17 pages, typeset with revtex4 and amsmath. Minor changes only. To appear in Commun. Math. Phys
References in corpus (2)
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