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

TL;DR

This paper investigates the low energy properties of the SU(m|n) supersymmetric Haldane-Shastry spin chain, revealing ground state degeneracies, linear dispersion relations, and connections to conformal field theories and other spin chains.

Contribution

It provides a detailed analysis of the ground state degeneracy, excitation spectrum, and conformal field theory description of the SU(m|n) Haldane-Shastry spin chain, including relations to the Polychronakos chain.

Findings

Ground state degeneracy is finite only for SU(m|0) and SU(m|1).

Low energy excitations have linear dispersion for all m, n.

SU(m|1) excitations are described by a conformal field theory of m Dirac fermions with central charge m/2.

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.