Anatomy of Abelian and Non-Abelian Fractional Quantum Hall States

B. Andrei Bernevig and N. Regnault
Phys. Rev. Lett. 103, 206801 – Published 10 November 2009

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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  • Received 28 March 2009

DOI:https://doi.org/10.1103/PhysRevLett.103.206801

©2009 American Physical Society

Authors & Affiliations

B. Andrei Bernevig1 and N. Regnault2

  • 1Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
  • 2Laboratoire Pierre Aigrain, Departement de Physique, ENS, CNRS, 24 rue Lhomond, 75005 Paris, France

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Issue

Vol. 103, Iss. 20 — 13 November 2009

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