Exact partition function of SU(m|n) supersymmetric Haldane-Shastry spin chain

Abstract

By taking the freezing limit of a spin Calogero-Sutherland model containing `anyon like' representation of the permutation algebra, we derive the exact partition function of SU(m|n) supersymmetric Haldane-Shastry (HS) spin chain. This partition function allows us to study global properties of the spectrum like level density distribution and nearest neighbour spacing distribution. It is found that, for supersymmetric HS spin chains with large number of lattice sites, continuous part of the energy level density obeys Gaussian distribution with a high degree of accuracy. The mean value and standard deviation of such Gaussian distribution can be calculated exactly. We also conjecture that the partition function of supersymmetric HS spin chain satisfies a duality relation under the exchange of bosonic and fermionic spin degrees of freedom.

arXiv commentLatex, 32 pages, 4 figures, minor typos corrected, to be published in Nucl. Phys. B

References in corpus (11)

• Yang-Baxter equation in spin chains with long range interactions
• Physics and Mathematics of Calogero particles
• Lattice Integrable Systems of Haldane-Shastry Type
• Solution of Some Integrable One-Dimensional Quantum Systems
• Exact Spectrum of SU(n) Spin Chain with Inverse-Square Exchange
• Global properties of the spectrum of the Haldane-Shastry spin chain
• Supersymmetric Polychronakos Spin Chain: Motif, Distribution Function, and Character
• Exact spectrum and partition function of SU(m|n) supersymmetric Polychronakos model
• Spin dependent extension of Calogero-Sutherland model through anyon like representations of permutation operators
• Symmetries and exact solutions of some integrable Haldane-Shastry like spin chains
• $gl(n|m)$ color Calogero-Sutherland models and Super Yangian Algebra

Cited by in corpus (35)

• Remarks on the notion of quantum integrability
• Low energy properties of the SU(m|n) supersymmetric Haldane-Shastry spin chain
• Infinite Matrix Product States for long range SU(N) spin models
• 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
• Boson-fermion duality in SU(m|n) supersymmetric Haldane-Shastry spin chain
• An exactly solvable supersymmetric spin chain of BC_N type
• On the level density of spin chains of Haldane--Shastry type
• Inozemtsev's hyperbolic spin model and its related spin chain
• Thermodynamics of spin chains of Haldane-Shastry type and one-dimensional vertex models
• Solitons in a continuous classical Haldane-Shastry spin chain
• Yangian-invariant spin models and Fibonacci numbers
• 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
• Thermodynamics and criticality of supersymmetric spin chains with long-range interactions
• One-Dimensional Vertex Models Associated with a Class of Yangian Invariant Haldane-Shastry Like Spin Chains
• Elliptic generalization of integrable q-deformed anisotropic Haldane-Shastry long-range spin chain
• 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
• Critical behavior of su(1|1) supersymmetric spin chains with long-range interactions
• Spin chains of Haldane-Shastry type and a generalized central limit theorem
• Level density distribution for one-dimensional vertex models related to Haldane-Shastry like spin chains
• $1/f^{\alpha }$ noise and integrable systems
• Partition functions of Polychronakos like spin chains associated with polarized spin reversal operators
• A novel quasi-exactly solvable spin chain with nearest-neighbors interactions
• Inequivalent quantization of the rational Calogero model with a Coulomb type interaction
• Appearance of branched motifs in the spectra of $B{C}_N$ type Polychronakos spin chains
• Supersymmetric analogue of BC_N type rational integrable models with polarized spin reversal operators
• A novel class of translationally invariant spin chains with long-range interactions
• The open Haldane-Shastry chain: thermodynamics and criticality
• Supersymmetric generalization of q-deformed long-range spin chains of Haldane-Shastry type and trigonometric GL(N|M) solution of associative Yang-Baxter equation
• Rational quantum integrable systems of D_N type with polarized spin reversal operators
• Supersymmetric $t$-$J$ models with long-range interactions: partition function and spectrum
• Super Rogers-Szegö polynomials associated with $B{C}_N$ type of Polychronakos spin chains