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arXiv · 0807.1495

An exactly solvable supersymmetric spin chain of BC_N type

J. C. Barba·F. Finkel·A. Gonzalez-Lopez·M. A. Rodriguez
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Abstract

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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J. C. Barba, F. Finkel, A. Gonzalez-Lopez, M. A. Rodriguez. 2008-07-09. An exactly solvable supersymmetric spin chain of BC_N type. https://doi.org/10.1016/j.nuclphysb.2008.08.014

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