An exactly solvable supersymmetric spin chain of BC_N type



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Barba, J. C: and Finkel Morgenstern, Federico and González López, Artemio and Rodríguez González, Miguel Ángel (2009) An exactly solvable supersymmetric spin chain of BC_N type. Nuclear physics B, 806 (3). pp. 684-714. ISSN 0550-3213

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We construct a new exactly solvable supersymmetric spin chain related to the BC_N extended root system, which includes as a particular case the BC_N version of the Polychronakos-Frahm spin chain. We also introduce a supersymmetric spin dynamical model of Calogero type which yields the new chain in the large coupling limit. This connection is exploited to derive two different closed-form expressions for the chain's partition function by means of Polychronakos's freezing trick. We establish a boson-fermion duality relation for the new chain's spectrum, which is in fact valid for a large class of (not necessarily integrable) spin chains of BC_N type. The exact expressions for the partition function are also used to study the chain's spectrum as a whole, showing that the level density is normally distributed even for a moderately large number of particles. We also determine a simple analytic approximation to the distribution of normalized spacings between consecutive levels which fits the numerical data with remarkable accuracy. Our results provide further evidence that spin chains of Haldane-Shastry type are exceptional integrable models, in the sense that their spacings distribution is not Poissonian, as posited by the Berry-Tabor conjecture for "generic" quantum integrable systems.

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©2008 Elsevier B.V. All fights reserved.
This work was partially supported by the DGI under grant No. FIS2005-00752, and by the Complutense University of Madrid and the DGUI under grant No. GR74/07-910556. J.C.B. acknowledges the financial support of the Spanish Ministry of Science and Innovation through an FPU scholarship.

Uncontrolled Keywords:Exactly solvable spin chains; Supersymmetry; Quantum chaos
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:31338
Deposited On:14 Jul 2015 15:12
Last Modified:10 Dec 2018 15:09

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