An exactly solvable supersymmetric spin chain of BC_N type
| Autor: | Barba, J. C., Finkel, F., Gonzalez-Lopez, A., Rodriguez, M. A. |
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| Rok vydání: | 2008 |
| Předmět: | |
| Zdroj: | Nucl.Phys.B806:684-714,2009 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.nuclphysb.2008.08.014 |
| Popis: | 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. Comment: 36 pages, 7 figures |
| Databáze: | arXiv |
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