Quasiparticle agglomerates in the Read–Rezayi and anti-Read–Rezayi states

Abstract

We calculate the dominant excitations for the k-level () Read–Rezayi (RR) states and their particle–hole conjugates, the anti-Read–Rezayi (), proposed for quantum Hall states. These states are supposed to be built over the second Landau level with total filling factor ν = 2 + ν* with ν* = k/(k + 2) for RR and ν* = 2/(k + 2) for . In the k-level RR states, based on parafermions, the dominant excitations are the fundamental quasiparticles (qps) with fractional charge e*k = e/(k + 2), with e the electron charge, if k = 2,3. For k = 4 the single-qp and the 2-agglomerate, with charge 2e*k, have the same scaling and both dominate, while for k > 4 the 2-agglomerates are dominant. Anyway the dominance of the 2-agglomerates can be affected by the presence of environmental renormalizations. For all the k-level states, the single-qp and the 2-agglomerate have the same scaling and both dominate. In this case, only the presence of environmental renormalizations can make one dominant over the other. We determine the conditions in which the environmental renormalizations of the charged and neutral modes make the Abelian 2-agglomerates dominant over the non-Abelian single-qps in the two models and for any value of k. We conclude by observing that, according to these predictions, the dominance of 2-agglomerates, at very low energies for the ν = 5/2, can be an interesting indication supporting the validity of the anti-Pfaffian model in comparison with the Pfaffian.