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 ⩾ 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.
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