Spin chains of Haldane-Shastry type and a generalized central limit theorem

Abstract

We show that the density of energy levels of a wide class of finite-dimensional quantum systems tends to a Gaussian distribution as the number of degrees of freedom increases. Our result is based on a nontrivial modification of the classical central limit theorem, and is especially suited to models whose partition function is explicitly known. In particular, we provide the first theoretical explanation of the fact that the level density of several spin chains of Haldane-Shastry type is asymptotically Gaussian when the number of sites tends to infinity.

RevTeX, 5 pages

References in corpus (7)

• Physics and Mathematics of Calogero particles
• 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

Cited by in corpus (6)

• On the level density of spin chains of Haldane--Shastry type
• Inozemtsev's hyperbolic spin model and its related spin chain
• Thermodynamics and criticality of supersymmetric spin chains with long-range interactions
• Exact solution and thermodynamics of a spin chain with long-range elliptic interactions
• $1/f^{\alpha }$ noise and integrable systems
• Generalized Lipkin-Meshkov-Glick models of Haldane-Shastry type