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.

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

References in corpus (3)

• Physics and Mathematics of Calogero particles
• Exact partition function of SU(m|n) supersymmetric Haldane-Shastry spin chain
• Exact spin dynamics of the 1/r^2 supersymmetric t-J model in a magnetic field

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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
• Superconformal Quantum Mechanics from M2-branes
• Supersymmetric spin chains with non-monotonic dispersion relation: criticality and entanglement entropy
• The open Haldane-Shastry chain: thermodynamics and criticality
• Rational quantum integrable systems of D_N type with polarized spin reversal operators
• Appearance of branched motifs in the spectra of $B{C}_N$ type Polychronakos spin chains
• Thermodynamics and criticality of su($m$) spin chains of Haldane-Shastry type
• Generalized Lipkin-Meshkov-Glick models of Haldane-Shastry type