Construction of a paired wave function for spinless electrons at filling fraction ν=25

Steven H. Simon, E. H. Rezayi, N. R. Cooper, and I. Berdnikov
Phys. Rev. B 75, 075317 – Published 12 February 2007

Abstract

We construct a wave function, generalizing the well-known Moore-Read Pfaffian, that describes spinless electrons at filling fraction ν=25 (or bosons at filling fraction ν=23) as the ground state of a very simple three body potential. We find, analogous to the Pfaffian, that when quasiholes are added there is a ground state degeneracy which can be identified as zero modes of the quasiholes. The zero modes are identified as having semionic statistics. We write this wave function as a correlator of the Virasoro minimal model conformal field theory M(5,3). Since this model is nonunitary, we conclude that this wave function is likely a quantum critical state. Nonetheless, we find that the overlaps of this wave function with exact diagonalizations in the lowest and first excited Landau level are very high, suggesting that this wave function may have experimental relevance for some transition that may occur in that regime.

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  • Received 17 August 2006

DOI:https://doi.org/10.1103/PhysRevB.75.075317

©2007 American Physical Society

Authors & Affiliations

Steven H. Simon1, E. H. Rezayi2, N. R. Cooper3, and I. Berdnikov1,4

  • 1Alcatel-Lucent, Bell Labs, Murray Hill, New Jersey 07974, USA
  • 2Department of Physics, California State University, Los Angeles, California 90032, USA
  • 3T. C. M. Group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
  • 4Department of Physics, Rutgers University, 136 Frelinghuysen Road, Piscataway, New Jersey 08854, USA

See Also

Generalized quantum Hall projection Hamiltonians

Steven H. Simon, E. H. Rezayi, and Nigel R. Cooper
Phys. Rev. B 75, 075318 (2007)

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Vol. 75, Iss. 7 — 15 February 2007

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