Barba, J. C:Finkel Morgenstern, FedericoGonzález López, ArtemioRodríguez González, Miguel Ángel2023-06-202023-06-202009-01-110550-321310.1016/j.nuclphysb.2008.08.014https://hdl.handle.net/20.500.14352/44679©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.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.engAtribución 3.0 Españahttps://creativecommons.org/licenses/by/3.0/es/journal articlehttp://dx.doi.org/10.1016/j.nuclphysb.2008.08.014http://www.sciencedirect.comopen access51-73Exactly solvable spin chainsSupersymmetryQuantum chaosFísica-Modelos matemáticosFísica matemática