RT Journal Article
T1 An exactly solvable supersymmetric spin chain of BC_N type
A1 Barba, J. C:
A1 Finkel Morgenstern, Federico
A1 González López, Artemio
A1 Rodríguez González, Miguel Ángel
AB 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.
PB Elsevier
SN 0550-3213
YR 2009
FD 2009-01-11
LK https://hdl.handle.net/20.500.14352/44679
UL https://hdl.handle.net/20.500.14352/44679
LA eng
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NO ©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.
NO DGI
NO Complutense University of Madrid
NO DGUI
NO Spanish Ministry of Science  and Innovation
DS Docta Complutense
RD 15 may 2024