The spin Sutherland model of D_N type and its associated spin chain

TL;DR

This paper introduces a new D_N type spin Sutherland model and its associated spin chain, providing exact spectra and partition functions, highlighting their distinct properties from known models.

Contribution

It presents the first analysis of the D_N type spin Sutherland model and derives its exact spectrum and partition function, expanding understanding of these complex integrable systems.

Findings

Exact spectrum of the D_N type spin Sutherland model obtained.

Partition function of the associated spin chain explicitly derived.

Model properties differ from BC_N counterparts and rational cases.

Abstract

In this paper we study the su(m) spin Sutherland (trigonometric) model of D_N type and its related spin chain of Haldane-Shastry type obtained by means of Polychronakos's freezing trick. As in the rational case recently studied by the authors, we show that these are new models, whose properties cannot be simply deduced from those of their well-known BC_N counterparts by taking a suitable limit. We identify the Weyl-invariant extended configuration space of the spin dynamical model, which turns out to be the N-dimensional generalization of a rhombic dodecahedron. This is in fact one of the reasons underlying the greater complexity of the models studied in this paper in comparison with both their rational and BC_N counterparts. By constructing a non-orthogonal basis of the Hilbert space of the spin dynamical model on which its Hamiltonian acts triangularly, we compute its spectrum in closed form. Using this result and applying the freezing trick, we derive an exact expression for the partition function of the associated Haldane-Shastry spin chain of D_N type.