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Haldane-Shastry spin chains of BCN type

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Enciso, Alberto and Finkel Morgenstern, Federico and González López, Artemio and Rodríguez González, Miguel Ángel (2005) Haldane-Shastry spin chains of BCN type. Nuclear physics B, 707 (3). pp. 553-576. ISSN 0550-3213

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Official URL: http://dx.doi.org/10.1103/PhysRevB.72.174411


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Abstract

We introduce four types of SU(2M + 1) spin chains which can be regarded as the BCN versions of the celebrated Haldane-Shastry chain. These chains depend on two free parameters and, unlike the original Haldane-Shastry chain, their sites need not be equally spaced. We prove that all four chains are solvable by deriving an exact expression for their partition function using Polychronakos's "freezing trick". From this expression we deduce several properties of the spectrum, and advance a number of conjectures that hold for a wide range of values of the spin M and the number of particles. In particular, we conjecture that the level density is Gaussian, and provide a heuristic derivation of general formulas for the mean and the standard deviation of the energy


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©2004 Elsevier B.V All rights reserved.
This work was partially supported by the DGI under grant No. BFM2002–02646. A.E. acknowledges the financial support of the Spanish Ministry of Education and Science through an FPU scholarship. The authors would like to thank J. Retamosa for pointing out Ref. [30] to them.

Uncontrolled Keywords:Spin chains; Exact solvability; Integrability; Calogero–Sutherland models; Dunkl operators
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:31378
Deposited On:14 Jul 2015 15:42
Last Modified:10 Dec 2018 15:09

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