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arXiv · 0707.3637

Fractional Quantum Hall States and Jack Polynomials

B. Andrei Bernevig·F. D. M. Haldane
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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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B. Andrei Bernevig, F. D. M. Haldane. 2007-08-14. Fractional Quantum Hall States and Jack Polynomials. https://doi.org/10.1103/physrevlett.100.246802

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