Fractional Quantum Hall States at ν=13/5 and 12/5 and Their Non-Abelian Nature

W. Zhu, S. S. Gong, F. D.M. Haldane, D. N. Sheng

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43 Scopus citations


Topological quantum states with non-Abelian Fibonacci anyonic excitations are widely sought after for the exotic fundamental physics they would exhibit, and for universal quantum computing applications. The fractional quantum Hall (FQH) state at a filling factor of ν=12/5 is a promising candidate; however, its precise nature is still under debate and no consensus has been achieved so far. Here, we investigate the nature of the FQH ν=13/5 state and its particle-hole conjugate state at 12/5 with the Coulomb interaction, and we address the issue of possible competing states. Based on a large-scale density-matrix renormalization group calculation in spherical geometry, we present evidence that the essential physics of the Coulomb ground state (GS) at ν=13/5 and 12/5 is captured by the k=3 parafermion Read-Rezayi state (RR3), including a robust excitation gap and the topological fingerprint from the entanglement spectrum and topological entanglement entropy. Furthermore, by considering the infinite-cylinder geometry (topologically equivalent to torus geometry), we expose the non-Abelian GS sector corresponding to a Fibonacci anyonic quasiparticle, which serves as a signature of the RR3 state at 13/5 and 12/5 filling numbers.

Original languageEnglish (US)
Article number126805
JournalPhysical review letters
Issue number12
StatePublished - Sep 18 2015

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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