Fibonacci anyons and charge density order in the 12/5 and 13/5 quantum Hall plateaus

Roger S.K. Mong, Michael P. Zaletel, Frank Pollmann, Zlatko Papić

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34 Scopus citations


The ν=12/5 fractional quantum Hall plateau observed in GaAs semiconductor wells is a suspect in the search for non-Abelian Fibonacci anyons. Using the infinite density matrix renormalization group, we find clear evidence that fillings ν=12/5 and ν=13/5 are in the k=3 Read-Rezayi phase in the absence of particle-hole symmetry breaking effects. The lowest energy charged excitation is identified as a non-Abelian Fibonacci anyon, distinguished from its Abelian counterpart by its local quadrupole moment. However, several experiments at ν=13/5 observe a reentrant integer quantum Hall effect, implying particle-hole symmetry is broken. We rule out spin polarization as the origin of the asymmetry. Further, we point out extremely close energetic competition between the Read-Rezayi phase and a reentrant integer quantum Hall phase. This competition suggests that even small particle-hole symmetry breaking perturbations can explain the experimentally observed asymmetry between ν=12/5 and 13/5. We find that at ν=12/5 Landau level mixing favors the Read-Rezayi phase over the reentrant phase.

Original languageEnglish (US)
Article number115136
JournalPhysical Review B
Issue number11
StatePublished - Mar 20 2017

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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