title: Fractional Quantum Hall States at ν=13/5 and 12/5 and Their Non-Abelian Nature.
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 (RR_{3}), 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 RR_{3} state at 13/5 and 12/5 filling numbers.
authors.affiliation: Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.|Department of Physics and Astronomy, California State University, Northridge, California 91330, USA.
authors.forename: W
authors.initials: W
authors.lastname: Zhu
authors.affiliation: Department of Physics and Astronomy, California State University, Northridge, California 91330, USA.
authors.forename: S S
authors.initials: SS
authors.lastname: Gong
authors.affiliation: Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: F D M
authors.initials: FD
authors.lastname: Haldane
authors.affiliation: Department of Physics and Astronomy, California State University, Northridge, California 91330, USA.
authors.forename: D N
authors.initials: DN
authors.lastname: Sheng