Polychronakos-Frahm spin chain of BC_N type and the Berry-Tabor conjecture



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Barba, J. C: and Finkel Morgenstern, Federico and González López, Artemio and Rodríguez González, Miguel Ángel (2008) Polychronakos-Frahm spin chain of BC_N type and the Berry-Tabor conjecture. Physical review B, 77 (21). ISSN 1098-0121

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Official URL: http://dx.doi.org/10.1103/PhysRevB.77.214422


We compute the partition function of the su(m) Polychronakos-Frahm spin chain of BC_N type by means of the freezing trick. We use this partition function to study several statistical properties of the spectrum, which turn out to be analogous to those of other spin chains of Haldane-Shastry type. In particular, we find that when the number of particles is sufficiently large the level density follows a Gaussian distribution with great accuracy. We also show that the distribution of (normalized) spacings between consecutive levels is of neither Poisson nor Wigner type but is qualitatively similar to that of the original Haldane-Shastry spin chain. This suggests that spin chains of Haldane-Shastry type are exceptional integrable models since they do not satisfy a well-known conjecture of Berry and Tabor, according to which the spacings distribution of a generic integrable system should be Poissonian. We derive a simple analytic expression for the cumulative spacings distribution of the BC_N-type Polychronakos-Frahm chain using only a few essential properties of its spectrum such as the Gaussian character of the level density and the fact that the energy levels are equally spaced. This expression is shown to be in excellent agreement with the numerical data.

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©2008 The American Physical Society.
This work was partially supported by the DGI under Grant No. FIS2005-00752, and by Complutense University 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.

Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:31340
Deposited On:14 Jul 2015 15:20
Last Modified:10 Dec 2018 15:09

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