Low energy properties of the SU(m|n) supersymmetric Haldane-Shastry spin chain

Abstract

The ground state and low energy excitations of the SU(m|n) supersymmetric Haldane-Shastry spin chain are analyzed. In the thermodynamic limit, it is found that the ground state degeneracy is finite only for the SU(m|0) and SU(m|1) spin chains, while the dispersion relation for the low energy and low momentum excitations is linear for all values of m and n. We show that the low energy excitations of the SU(m|1) spin chain are described by a conformal field theory of m non-interacting Dirac fermions which have only positive energies; the central charge of this theory is m/2. Finally, for n \ge 1, the partition functions of the SU(m|n) Haldane-Shastry spin chain and the SU(m|n) Polychronakos spin chain are shown to be related in a simple way in the thermodynamic limit at low temperatures.

arXiv comment40 pages including 2 figures; added some references; this version will appear in Nuclear Physics B

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• An exactly solvable supersymmetric spin chain of BC_N type
• Inozemtsev's hyperbolic spin model and its related spin chain
• 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
• Yangian-invariant spin models and Fibonacci numbers
• Quasi exactly solvable extension of Calogero model associated with exceptional orthogonal polynomials
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• One-Dimensional Vertex Models Associated with a Class of Yangian Invariant Haldane-Shastry Like Spin Chains
• 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
• Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions
• Superconformal Quantum Mechanics from M2-branes
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• 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
• Supersymmetric analogue of BC_N type rational integrable models with polarized spin reversal operators
• The open Haldane-Shastry chain: thermodynamics and criticality
• Super Rogers-Szegö polynomials associated with $B{C}_N$ type of Polychronakos spin chains
• Supersymmetric $t$-$J$ models with long-range interactions: thermodynamics and criticality
• Thermodynamics and criticality of su($m$) spin chains of Haldane-Shastry type
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