The spin Sutherland model of D-N type and its associated spin chain



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Basu-Mallick, B. and Finkel Morgenstern, Federico and González López, Artemio (2011) The spin Sutherland model of D-N type and its associated spin chain. Nuclear physics B, 843 (3). pp. 505-533. ISSN 0550-3213

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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 BCN 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 BCN 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.

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©2010 Elsevier B.V. All rights reserved.
This work was supported in part by the MICINN and the UCM–Banco Santander under Grants Nos. FIS2008-00209 and GR58/08-910556. The authors would also like to thank A. Enciso for several helpful discussions.

Uncontrolled Keywords:Exactly solvable spin models; Spin chains; Dunkl operators
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:31277
Deposited On:02 Jul 2015 15:22
Last Modified:10 Dec 2018 15:09

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