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.

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

References in corpus (1)

• Physics and Mathematics of Calogero particles

Cited by in corpus (7)

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• 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
• One-Dimensional Vertex Models Associated with a Class of Yangian Invariant Haldane-Shastry Like Spin Chains
• A novel quasi-exactly solvable spin chain with nearest-neighbors interactions