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

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

2002-02-13

arxiv.org/abs/hep-th/0202080v3

Commun.Math.Phys. 233 (2003) 191-209

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1007/s00220-002-0742-z

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".

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