Non-Abelian phases from the condensation of Abelian anyons

TL;DR

This paper demonstrates that condensing clusters of Abelian anyons in fractional quantum Hall states can produce non-Abelian phases, providing a new pathway to realize complex topological states with potential applications in quantum computing.

Contribution

It introduces a novel method of generating non-Abelian fractional quantum Hall states through the condensation of quasiparticle clusters, supported by theoretical and numerical evidence.

Findings

Condensing quasiparticle pairs in the $ u=2/3$ Laughlin state yields the anti-Pfaffian phase.

Successive condensation of Laughlin quasiparticles produces states matching prominent Landau level plateaus.

The method can realize any non-Abelian FQH state with a parton representation.

Abstract

The observed fractional quantum Hall (FQH) plateaus follow a recurring hierarchical structure that allows an understanding of complex states based on simpler ones. Condensing the elementary quasiparticles of an Abelian FQH state results in a new Abelian phase at a different filling factor, and this process can be iterated \textit{ad infinitum}. We show that condensing clusters of the same quasiparticles into an Abelian state can instead realize non-Abelian FQH states. In particular, condensing quasiparticle pairs in the $\nu=\frac{2}{3}$ Laughlin state yields the anti-Pfaffian phase at half-filling. We moreover show that the successive condensation of Laughlin quasiparticles produces quantum Hall states whose fillings coincide with the most prominent plateaus in the first excited Landau level of GaAs. More generally, such condensation can realize any non-Abelian FQH state that admits a parton representation. This surprising result is supported by an exact analysis of explicit wavefunctions, field theory arguments, conformal-field theory constructions of trial states, and numerical simulations.