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The Anatomy of Abelian and Non-Abelian Fractional Quantum Hall States

By B. Andrei Bernevig and N. Regnault

Abstract

modify comment in Ref. 14International audienceWe 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 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

Topics: [PHYS.COND.CM-GEN] Physics [physics]/Condensed Matter [cond-mat]/Other [cond-mat.other]
Publisher: American Physical Society
Year: 2009
OAI identifier: oai:HAL:hal-00522234v1
Provided by: Hal-Diderot
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