Boson-fermion duality in SU(m|n) supersymmetric Haldane-Shastry spin chain

TL;DR

This paper demonstrates a boson-fermion duality in the SU(m|n) supersymmetric Haldane-Shastry spin chain using super Yangian symmetry, revealing a new combinatorial formula and linking global symmetry to duality.

Contribution

It introduces a duality relation for the partition function of the model and derives a novel combinatorial formula for super Schur polynomials, connecting symmetry and duality.

Findings

Partition function satisfies a boson-fermion duality relation.

Derived a new combinatorial formula for super Schur polynomials.

Connected SU(m|n) symmetry with the boson-fermion duality.

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.