Boson-fermion duality in SU(m|n) supersymmetric Haldane-Shastry spin chain
B. Basu-Mallick, Nilanjan Bondyopadhaya, Kazuhiro Hikami, Diptiman Sen
Abstract
By using the Y(gl(m|n)) super Yangian symmetry of the SU(m|n) supersymmetric Haldane-Shastry spin chain, we show that the partition function of this model satisfies a duality relation under the exchange of bosonic and fermionic spin degrees of freedom. As a byproduct of this study of the duality relation, we find a novel combinatorial formula for the super Schur polynomials associated with some irreducible representations of the Y(gl(m|n)) Yangian algebra. Finally, we reveal an intimate connection between the global SU(m|n) symmetry of a spin chain and the boson-fermion duality relation.
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