Condensing non-Abelian quasiparticles

TL;DR

This paper introduces a hierarchy scheme for constructing new fractional quantum Hall states by condensing non-Abelian quasiparticles, leading to daughter states with different non-Abelian statistics, exemplified by the $ u=4/3$ Moore-Read state.

Contribution

It presents a novel hierarchy method for generating daughter states with non-Abelian quasiparticles through condensation, expanding the understanding of fractional quantum Hall state constructions.

Findings

Daughter states have distinct non-Abelian statistics from parent states.

Explicit example provided for the $ u=4/3$ Moore-Read state.

Hierarchy scheme offers a new way to explore fractional quantum Hall phases.

Abstract

A most interesting feature of certain fractional quantum Hall states is that their quasiparticles obey non-Abelian fractional statistics. So far, candidate non-Abelian wave functions have been constructed from conformal blocks in cleverly chosen conformal field theories. In this work we present a hierarchy scheme by which we can construct daughter states by condensing non-Abelian quasiparticles (as opposed to quasiholes) in a parent state, and show that the daughters have a non-Abelian statistics that differ from the parent. In particular, we discuss the daughter of the bosonic, spin-polarized Moore-Read state at $\nu=4/3$ as an explicit example.