Boson–fermion duality in SU(mn) supersymmetric Haldane–Shastry spin chain
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摘要
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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