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

TL;DR

This paper demonstrates the integrability of the B_N hyperbolic Sutherland spin model and explicitly computes its spectrum by leveraging Dunkl operators and the freezing trick, advancing understanding of spin chain models.

Contribution

It introduces a new integrability proof for the B_N hyperbolic Sutherland spin model using Dunkl operators and explicitly calculates the spectrum of the associated spin chain.

Findings

Complete family of commuting integrals established

Explicit spectrum computed via triangularization

Integrability proved using the freezing trick

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".