Integrable N-particle Hamiltonians with Yangian or Reflection Algebra Symmetry

Abstract

We use the Dunkl operator approach to construct one dimensional integrable models describing N particles with internal degrees of freedom. These models are described by a general Hamiltonian belonging to the center of the Yangian or the reflection algebra, which ensures that they admit the corresponding symmetry. In particular, the open problem of the symmetry is answered for the B_N-type Sutherland model with spin and a generalized B_N-type nonlinear Schrodinger Hamiltonian.

17 pages. Some typos corrected, references added and proofs clarified

References in corpus (10)

• Exchange Operator Formalism for Integrable Systems of Particles
• Yang-Baxter equation in spin chains with long range interactions
• Explicit Solution to the N-Body Calogero Problem
• Integrable Systems for Particles with Internal Degrees of Freedom
• Representations of reflection algebras
• A_N-type Dunkl operators and new spin Calogero-Sutherland models
• New spin Calogero-Sutherland models related to B_N-type Dunkl operators
• Yangian symmetry in the Non Linear Schrodinger hierarchy
• Yangians, finite W-algebras and the Non Linear Schrodinger hierarchy
• On the Sutherland Spin Model of B_N Type and its Associated Spin Chain

Cited by in corpus (11)

• Some aspects of jump-defects in the quantum sine-Gordon model
• Haldane-Shastry spin chains of BC_N type
• Set-theoretical reflection equation: Classification of reflection maps
• On reflection algebras and twisted Yangians
• Exact results for the one-dimensional many-body problem with contact interaction: Including a tunable impurity
• Twisted spin Sutherland models from quantum Hamiltonian reduction
• Sutherland Models for Complex Reflection Groups
• Partition functions of Polychronakos like spin chains associated with polarized spin reversal operators
• Classical $N$-Reflection Equation and Gaudin Models
• How to fold a spin chain: Integrable boundaries of the Heisenberg XXX and Inozemtsev hyperbolic models
• Supersymmetric analogue of BC_N type rational integrable models with polarized spin reversal operators