Abelian and non-Abelian statistics in the coherent state representation

TL;DR

This paper develops a unified approach to identify Abelian and non-Abelian braiding statistics in fractional quantum Hall states using adiabatic transport and coherent states, providing intuitive insights and verifying results for complex states.

Contribution

It introduces a refined method to determine braiding statistics that applies to both Abelian and non-Abelian states without additional assumptions.

Findings

Applicable to Laughlin and Moore-Read states

Successfully extended to level 3 Read-Rezayi state

Provides intuitive topological sector transformation pictures

Abstract

We further develop an approach to identify the braiding statistics associated to a given fractional quantum Hall state through adiabatic transport of quasiparticles. This approach is based on the notion of adiabatic continuity between quantum Hall states on the torus and simple product states---or "patterns"---in the thin torus limit, together with a suitable coherent state Ansatz for localized quasiholes that respects the modular invariance of the torus. We give a refined and unified account of the application of this method to the Laughlin and Moore-Read states, which may serve as a pedagogical introduction to the nuts and bolts of this technique. Our main result is that the approach is also applicable---without further assumptions---to more complicated non-Abelian states. We demonstrate this in great detail for the level $k=3$ Read-Rezayi state at filling factor $\nu=3/2$. These results may serve as an independent check of other techniques, where the statistics are inferred from conformal block monodromies. Our approach has the benefit of giving rise to intuitive pictures representing the transformation of topological sectors during braiding, and allows for a self-consistent derivation of non-Abelian statistics without heavy mathematical machinery.