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arXiv:cond-mat/0110108 · Journal of Physics A Mathematical and General

Parafermion statistics and application to non-Abelian quantum Hall states

Eddy Ardonne

Published Jan 14, 2002• 28 citations
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Abstract

The (exclusion) statistics of parafermions is used to study degeneracies of quasiholes over the paired (or in general clustered) quantum Hall states. The focus is on the ℤ k and 𝔰𝔲(3) k /𝔲(1) 2 parafermions, which are used in the description of spin-polarized and spin-singled clustered quantum Hall states.
DOI
10.1088/0305-4470/35/3/301

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It has long been known that, under the laws of quantum mechanics, particles in two spatial dimensions may exhibit non-abelian braid statistics. In this note we briefly discuss particular states of matter, so-called paired and clustered quantum Hall states, which offer a concrete realization of this scenario: quasi-holes over these quantum Hall states satisfy non-abelian braid statistics. The associated degeneracies have their origin in combinatorial properties of (para-)fermions in conformal field theory. We also discuss the exclusion statistics of edge excitations in these quantum Hall systems.
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We determine the exclusion statistics properties of the fundamental edge quasiparticles over a specific $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{1}{2}$ non-Abelian quantum Hall state known as the q=2q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2q=2 Pfaffian state. The fundamental excitations are the edge electrons of charge $\ensuremath{-}e$ and the edge quasiholes of charge +e/4+e/4+e/4. We explicitly determine thermodynamic distribution functions and establish a duality which generalizes the duality for fractional exclusion statistics as described by F. D. M. Haldane.