Fractional Quantum Hall States atν=13/5and12/5and Their Non-Abelian Nature

2015/05/31 by Wei Zhu, W. Zhu, Shou-Shu Gong +3 · 2 citations
Mathematics · Physics and Astronomy · #Combinatorics #Electron #Fibonacci number #Fractional quantum Hall effect #Mathematics #Physics #Quantum #Quantum Hall effect #Quantum and electron transport phenomena #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Quantum spin Hall effect #Quasiparticle #Superconductivity #Topological Materials and Phenomena #Topological insulator #Topological order #Topology (electrical circuits) #cond-mat.mes-hall #cond-mat.str-el

paper · pdf · doi:10.1103/physrevlett.115.126805

published as Phys. Rev. Lett. 115, 126805 (2015) · 12 pages, 8 figures

arxiv created 2015/09/07 · openalex publication_date 2015/09/18 · arxiv updated 2015/09/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

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.

Citations

• Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations
• TOPOLOGICAL ORDERS IN RIGID STATES
• Two-Dimensional Magnetotransport in the Extreme Quantum Limit
• Fractional quantum Hall hierarchy and the second Landau level
• Detecting Topological Order in a Ground State Wave Function
• Topological quantum compiling
• Momentum polarization: An entanglement measure of topological spin and chiral central charge
• Ground-State Phase Diagram of 2D Electrons in a High Landau Level: A Density-Matrix Renormalization Group Study
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• Disentangling Entanglement Spectra of Fractional Quantum Hall States on Torus Geometries
• Non-Abelian anyons and topological quantum computation
• Comparison of the density-matrix renormalization group method applied to fractional quantum Hall systems in different geometries
• Nonabelions in the fractional quantum hall effect
• A Modular Functor Which is Universal¶for Quantum Computation

Cited by

• Fractional Quantum Hall Effects
• Evolution of quantum entanglement with disorder in fractional quantum Hall liquids