Issue
EPL
Volume 83, Number 2, July 2008
Article Number 27005
Number of page(s) 6
Section Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties
DOI http://dx.doi.org/10.1209/0295-5075/83/27005
Published online 27 June 2008
EPL, 83 (2008) 27005
DOI: 10.1209/0295-5075/83/27005

The Berry-Tabor conjecture for spin chains of Haldane-Shastry type

J. C. Barba, F. Finkel, A. González-López and M. A. Rodríguez

Departamento de Física Teórica II, Universidad Complutense - 28040 Madrid, Spain, EU

jcbarba@fis.ucm.es
ffinkel@fis.ucm.es
artemio@fis.ucm.es
rodrigue@fis.ucm.es

received 23 April 2008; accepted in final form 28 May 2008; published July 2008
published online 27 June 2008

Abstract
According to a long-standing conjecture of Berry and Tabor, the distribution of the spacings between consecutive levels of a "generic" integrable model should follow Poisson's law. In contrast, the spacings distribution of chaotic systems typically follows Wigner's law. An important exception to the Berry-Tabor conjecture is the integrable spin chain with long-range interactions introduced by Haldane and Shastry in 1988, whose spacings distribution is neither Poissonian nor of Wigner's type. In this letter we argue that the cumulative spacings distribution of this chain should follow the "square root of a logarithm" law recently proposed by us as a characteristic feature of all spin chains of Haldane-Shastry type. We also show in detail that the latter law is valid for the rational counterpart of the Haldane-Shastry chain introduced by Polychronakos.

PACS
75.10.Pq - Spin chain models.
05.45.Mt - Quantum chaos; semiclassical methods.

© EPLA 2008