Search for electron liquids with non-Abelian quasiparticles

TL;DR

This paper investigates fractional quantum Hall states with non-Abelian quasiparticles using numerical methods, identifying promising states at specific filling factors and validating the composite fermion model outside this range.

Contribution

It provides numerical evidence for non-Abelian quantum Hall states at certain filling factors and clarifies the nature of states outside this range, including their relation to Laughlin liquids.

Findings

Supports non-Abelian candidates at ν_e=5/2 and 12/5.

Validates Abelian composite fermion liquids outside the non-Abelian range.

Shows the ν_e=7/3 state is connected to the Laughlin liquid but with different correlations.

Abstract

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 $7/3 <\nu_e<8/3$. 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 $\nu_e=5/2$ (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 $\nu_e=7/3$ state is shown to be adiabatically connected to the Laughlin liquid, but its short-range correlations are significantly different.