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

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.

LaTeX, 30 pages

References in corpus (8)

• Physics and Mathematics of Calogero particles
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• The Polychronakos-Frahm spin chain of BC_N type and Berry-Tabor's conjecture
• The Berry-Tabor conjecture for spin chains of Haldane-Shastry type
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Cited by in corpus (9)

• On the level density of spin chains of Haldane--Shastry type
• Thermodynamics of spin chains of Haldane-Shastry type and one-dimensional vertex models
• The exactly solvable spin Sutherland model of B_N type and its related spin chain
• Thermodynamics and criticality of supersymmetric spin chains with long-range interactions
• The open Haldane-Shastry chain: thermodynamics and criticality
• A novel class of translationally invariant spin chains with long-range interactions
• Supersymmetric analogue of BC_N type rational integrable models with polarized spin reversal operators
• Rational quantum integrable systems of D_N type with polarized spin reversal operators
• Generalized Calogero-Sutherland models for Kondo physics in the Luttinger liquid