2009/11/29 by Arkadiusz Wojs, Arkadiusz Wójs
Physics and Astronomy · #Composite fermion #Fermion #Fractional quantum Hall effect #Landau quantization #Physics of Superconductivity and Magnetism #Quantum Hall effect #Quantum and electron transport phenomena #Quasiparticle #Range (aeronautics) #Spectral line #Topological Materials and Phenomena #cond-mat.mes-hall #cond-mat.str-el
paper · pdf · doi:10.1088/1742-6596/213/1/012022
published as J. Phys.: Conf. Ser. 213, 012022 (2010) · 9 pages, 8 figures
arxiv created 2009/11/29 · openalex publication_date 2010/03/01 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We use exact numerical diagonalization in the search of fractional quantum Hall states with non-Abelian quasiparticle statistics. For the (most promising) states in a partially filled second Landau level, the search is narrowed to the range of filling factors 7/3 < v e < 8/3. In this range, the analysis of energy spectra and correlation functions, calculated including finite width and Landau level mixing, supports the prominent non-Abelian candidates at v e = 5/2 (paired Moore–Read "pfafian" state) and 12/5 (clustered Read–Rezayi "parafermion" state). Outside of this range, the noninteracting composite fermion model with four attached flux quanta is validated, yielding the family of quantum liquids with fractional, but Abelian statistics. The borderline v e = 7/3 state is shown to be adiabatically connected to the Laughlin liquid, but its short-range correlations are significantly different.