On the level density of spin chains of Haldane--Shastry type

Abstract

We provide a rigorous proof of the fact that the level density of all su(m) spin chains of Haldane-Shastry type associated with the A_{N-1} root system approaches a Gaussian distribution as the number of spins N tends to infinity. Our approach is based on the study of the large N limit of the characteristic function of the level density, using the description of the spectrum in terms of motifs and the asymptotic behavior of the dispersion relation.

6 pages, revtex

References in corpus (9)

• Exact partition function of SU(m|n) supersymmetric Haldane-Shastry spin chain
• Low energy properties of the SU(m|n) supersymmetric Haldane-Shastry spin chain
• The Polychronakos-Frahm spin chain of BC_N type and Berry-Tabor's conjecture
• The Berry-Tabor conjecture for spin chains of Haldane-Shastry type
• Exactly solvable D_N-type quantum spin models with long-range interaction
• An exactly solvable supersymmetric spin chain of BC_N type
• Inozemtsev's hyperbolic spin model and its related spin chain
• The spin Sutherland model of D_N type and its associated spin chain
• Spin chains of Haldane-Shastry type and a generalized central limit theorem

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• One-Dimensional Vertex Models Associated with a Class of Yangian Invariant Haldane-Shastry Like Spin Chains
• Thermodynamics and criticality of supersymmetric spin chains with long-range interactions
• A new perspective on the integrability of Inozemtsev's elliptic spin chain
• 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
• Partition functions of Polychronakos like spin chains associated with polarized spin reversal operators
• Supersymmetric analogue of BC_N type rational integrable models with polarized spin reversal operators
• Appearance of branched motifs in the spectra of $B{C}_N$ type Polychronakos spin chains
• The open Haldane-Shastry chain: thermodynamics and criticality
• A novel class of translationally invariant spin chains with long-range interactions
• Rational quantum integrable systems of D_N type with polarized spin reversal operators
• Super Rogers-Szegö polynomials associated with $B{C}_N$ type of Polychronakos spin chains
• Generalized Lipkin-Meshkov-Glick models of Haldane-Shastry type