### Abstract

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 language | English (US) |
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Article number | 126805 |

Journal | Physical review letters |

Volume | 115 |

Issue number | 12 |

DOIs | |

State | Published - Sep 18 2015 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

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## Cite this

*Physical review letters*,

*115*(12), [126805]. https://doi.org/10.1103/PhysRevLett.115.126805