Decomposition of fractional quantum Hall model states: Product rule symmetries and approximations

Ronny Thomale, Benoit Estienne, Nicolas Regnault, B. Andrei Bernevig

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


We provide a detailed description of a product rule structure of the monomial (Slater) expansion coefficients of bosonic (fermionic) fractional quantum Hall (FQH) states derived recently, which we now extend to spin-singlet states. We show that the Haldane-Rezayi spin-singlet state can be obtained without exact diagonalization through a differential equation method that we conjecture to be generic to other FQH model states. The product rule symmetries allow us to build approximations of FQH states that exhibit increasing overlap with the exact state (as a function of system size) even though our approximation omits more than half of the Hilbert space. We show that the product rule is valid for any FQH state that can be written as an expectation value of parafermionic operators.

Original languageEnglish (US)
Article number045127
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number4
StatePublished - Jul 19 2011

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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