Anatomy of abelian and non-abelian fractional quantum hall states

B. Andrei Bernevig, N. Regnault

Research output: Contribution to journalArticle

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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.

Original languageEnglish (US)
Article number206801
JournalPhysical review letters
Volume103
Issue number20
DOIs
StatePublished - Nov 10 2009

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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