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

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.

26 pages, no figures; corrected some typos

References in corpus (6)

• Physics and Mathematics of Calogero particles
• Enlarged symmetry algebras of spin chains, loop models, and S-matrices
• Exact partition function of SU(m|n) supersymmetric Haldane-Shastry spin chain
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• Exact two-holon wave functions in the Kuramoto-Yokoyama model
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• A novel class of translationally invariant spin chains with long-range interactions
• Rational quantum integrable systems of D_N type with polarized spin reversal operators
• Exact solution of $D_N$ type quantum Calogero model through a mapping to free harmonic oscillators
• Super Rogers-Szegö polynomials associated with $B{C}_N$ type of Polychronakos spin chains
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