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

Author(s): Zhu, W; Gong, SS; Haldane, Frederick D; Sheng, DN

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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 nu = 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 nu = 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 nu = 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 RR3 state at 13/5 and 12/5 filling numbers.
Publication Date: 18-Sep-2015
Electronic Publication Date: 18-Sep-2015
Citation: Zhu, W, Gong, SS, Haldane, FDM, Sheng, DN. (2015). Fractional Quantum Hall States at nu=13/5 and 12/5 and Their Non-Abelian Nature. PHYSICAL REVIEW LETTERS, 115 (10.1103/PhysRevLett.115.126805
DOI: doi:10.1103/PhysRevLett.115.126805
ISSN: 0031-9007
EISSN: 1079-7114
Type of Material: Journal Article
Journal/Proceeding Title: PHYSICAL REVIEW LETTERS
Version: Final published version. This is an open access article.

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