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

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.

LaTeX with revtex4, 6 pages, 6 figures

References in corpus (15)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Lattice Integrable Systems of Haldane-Shastry Type
• On Models with Inverse-Square Exchange
• Poisson versus GOE statistics in integrable and non-integrable quantum hamiltonian
• Integrable Systems for Particles with Internal Degrees of Freedom
• Exact Spectrum of SU(n) Spin Chain with Inverse-Square Exchange
• Spectrum of a spin chain with inverse square exchange
• Global properties of the spectrum of the Haldane-Shastry spin chain
• Exact partition function of SU(m|n) supersymmetric Haldane-Shastry spin chain
• Haldane-Shastry spin chains of BC_N type
• Integrable $1/r^2$ Spin Chain with Reflecting End
• Low energy properties of the SU(m|n) supersymmetric Haldane-Shastry spin chain
• Exact spectrum and partition function of SU(m|n) supersymmetric Polychronakos model
• The Polychronakos-Frahm spin chain of BC_N type and Berry-Tabor's conjecture
• Random Matrix Theory and higher genus integrability: the quantum chiral Potts model

Cited by in corpus (26)

• Remarks on the notion of quantum integrability
• Exactly solvable D_N-type quantum spin models with long-range interaction
• On the level density of spin chains of Haldane--Shastry type
• An exactly solvable supersymmetric spin chain of BC_N type
• Interacting Particles on the Line and Dunkl Intertwining Operator of Type A: Application to the Freezing Regime
• Inozemtsev's hyperbolic spin model and its related spin chain
• Thermodynamics of spin chains of Haldane-Shastry type and one-dimensional vertex models
• Long-range level correlations in quantum systems with finite Hilbert space dimension
• Spectral properties of supersymmetric Polychronakos spin chain associated with A_{N-1} root system
• Yangian-invariant spin models and Fibonacci numbers
• The spin Sutherland model of D_N type and its associated spin chain
• Thermodynamics and criticality of supersymmetric spin chains with long-range interactions
• A new perspective on the integrability of Inozemtsev's elliptic spin chain
• Spin chains of Haldane-Shastry type and a generalized central limit theorem
• Exact solution and thermodynamics of a spin chain with long-range elliptic interactions
• Level density distribution for one-dimensional vertex models related to Haldane-Shastry like spin chains
• $1/f^{\alpha }$ noise and integrable systems
• The Ergodicity Landscape of Quantum Theories
• Partition functions of Polychronakos like spin chains associated with polarized spin reversal operators
• The open Haldane-Shastry chain: thermodynamics and criticality
• Supersymmetric analogue of BC_N type rational integrable models with polarized spin reversal operators
• Rational quantum integrable systems of D_N type with polarized spin reversal operators
• Thermodynamics and criticality of su($m$) spin chains of Haldane-Shastry type
• Super Rogers-Szegö polynomials associated with $B{C}_N$ type of Polychronakos spin chains
• Generalized Lipkin-Meshkov-Glick models of Haldane-Shastry type
• Generalized Calogero-Sutherland models for Kondo physics in the Luttinger liquid