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

Ronny Thomale, Benoit Estienne, Nicolas Regnault, and B. Andrei Bernevig
Phys. Rev. B 84, 045127 – Published 19 July 2011

Abstract

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.

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  • Received 22 October 2010

DOI:https://doi.org/10.1103/PhysRevB.84.045127

©2011 American Physical Society

Authors & Affiliations

Ronny Thomale1, Benoit Estienne2, Nicolas Regnault3, and B. Andrei Bernevig1

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

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Issue

Vol. 84, Iss. 4 — 15 July 2011

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