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

Journal Article · Fri Jul 15 04:00:00 EDT 2011 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/PHYSREVB.84.045127· OSTI ID:21596833

Thomale, Ronny; Bernevig, B Andrei ^[1]; Estienne, Benoit ^[2]; Regnault, Nicolas ^[3]

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1. Department of Physics, Princeton University, Princeton, New Jersey 08544 (United States)
2. Institute for Theoretical Physics, Universiteit van Amsterdam Valckenierstraat 65, NL-1018 XE Amsterdam (Netherlands)
3. LPA, Departement de Physique, ENS, CNRS, 24 rue Lhomond, FR-75005 Paris (France)

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.

• OSTI ID: 21596833
• Journal Information: Physical Review. B, Condensed Matter and Materials Physics, Journal Name: Physical Review. B, Condensed Matter and Materials Physics Journal Issue: 4 Vol. 84; ISSN 1098-0121
• Country of Publication: United States
• Language: English

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