Fractional Quantum Hall States and Jack Polynomials

2007/07/31 by B. Andrei Bernevig, F. D. M. Haldane · 4 citations
Physics and Astronomy · #cond-mat.mes-hall

paper · pdf · doi:10.1103/physrevlett.100.246802

published as Phys. Rev. Lett. 100, 246802 (2008) · 4 pages, 2 figures 2 new references added

arxiv created 2007/08/14 · arxiv updated 2009/12/01

Abstract

We describe an occupation-number-like picture of Fractional Quantum Hall (FQH) states in terms of polynomial wavefunctions characterized by a dominant occupation-number configuration. The bosonic variants of single-component abelian and non-abelian FQH states are modeled by Jacks (Jack symmetric polynomials), characterized by dominant occupation-number configurations satisfying a generalized Pauli principle. In a series of well-known Quantum Hall states, including the Laughlin, Read-Moore, and Read-Rezayi, the Jack polynomials naturally implement a ``squeezing rule'' that constrains allowed configurations to be restricted to those obtained by squeezing the dominant configuration. The Jacks describing uniform FQH states satisfy a highest-weight condition, and a clustering condition which can be generalized to describe quasiparticle states.

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