Exactly solvable D_N-type quantum spin models with long-range interaction

Abstract

We derive the spectra of the D_N-type Calogero (rational) su(m) spin model, including the degeneracy factors of all energy levels. By taking the strong coupling limit of this model, in which its spin and dynamical degrees of freedom decouple, we compute the exact partition function of the su(m) Polychronakos-Frahm spin chain of D_N type. With the help of this partition function we study several statistical properties of the chain's spectrum, such as the density of energy levels and the distribution of spacings between consecutive levels.

12 pages, 2 figures

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• Thermodynamics of spin chains of Haldane-Shastry type and one-dimensional vertex models
• Spectral properties of supersymmetric Polychronakos spin chain associated with A_{N-1} root system
• The spin Sutherland model of D_N type and its associated spin chain
• The exactly solvable spin Sutherland model of B_N type and its related 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
• Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions
• Superconformal Quantum Mechanics from M2-branes
• Level density distribution for one-dimensional vertex models related to Haldane-Shastry like spin chains
• $1/f^{\alpha }$ noise and integrable systems
• Exact solution of $D_N$ type quantum Calogero model through a mapping to free harmonic oscillators
• A novel class of translationally invariant spin chains with long-range interactions
• Supersymmetric analogue of BC_N type rational integrable models with polarized spin reversal operators
• The open Haldane-Shastry chain: thermodynamics and criticality
• Appearance of branched motifs in the spectra of $B{C}_N$ type Polychronakos spin chains
• 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