Paper detail

Search for electron liquids with non-Abelian quasiparticles

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 $7/3 <ν_e<8/3$. 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 $ν_e=5/2$ (paired Moore--Read &#34;pfafian&#34; state) and 12/5 (clustered Read--Rezayi &#34;parafermion&#34; 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 $ν_e=7/3$ state is shown to be adiabatically connected to the Laughlin liquid, but its short-range correlations are significantly different.