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  • Title: Anatomy of Abelian and non-Abelian fractional quantum Hall states.
    Author: Bernevig BA, Regnault N.
    Journal: Phys Rev Lett; 2009 Nov 13; 103(20):206801. PubMed ID: 20365997.
    Abstract:
    We deduce a new set of symmetries and relations between the coefficients of the expansion of Abelian and non-Abelian fractional quantum Hall (FQH) states in free (bosonic or fermionic) many-body states. Our rules allow us to build an approximation of a FQH model state with an overlap increasing with growing system size (that may sometimes reach unity) while using a fraction of the original Hilbert space. We prove these symmetries by deriving a previously unknown recursion formula for all the coefficients of the Slater expansion of the Laughlin, Read-Rezayi, and many other states (all Jacks multiplied by Vandermonde determinants), which completely removes the current need for diagonalization procedures for these model Hamiltonians.
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