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, and D. N. Sheng
Phys. Rev. Lett. 115, 126805 – Published 18 September 2015
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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.

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  • Received 25 May 2015

DOI:https://doi.org/10.1103/PhysRevLett.115.126805

© 2015 American Physical Society

Authors & Affiliations

W. Zhu1,2, S. S. Gong2, F. D. M. Haldane1, and D. N. Sheng2

  • 1Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
  • 2Department of Physics and Astronomy, California State University, Northridge, California 91330, USA

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Vol. 115, Iss. 12 — 18 September 2015

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