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Fractional Quantum Hall States at ν = 13/5 and 12/5 and Their Non-Abelian Nature.
- Source :
-
Physical Review Letters . 9/18/2015, Vol. 115 Issue 12, p126805-1-126805-6. 6p. - Publication Year :
- 2015
-
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 sofar. 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00319007
- Volume :
- 115
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Physical Review Letters
- Publication Type :
- Academic Journal
- Accession number :
- 110283701
- Full Text :
- https://doi.org/10.1103/PhysRevLett.115.126805