How SU(2)$_4$ Anyons are Z$_3$ Parafermions

Fern, Richard; Kombe, Johannes; Simon, Steven

doi:10.21468/SciPostPhys.3.6.037

SciPost Physics

How SU(2)$_4$ Anyons are Z$_3$ Parafermions

Richard Fern, Johannes Kombe, Steven H. Simon

SciPost Phys. 3, 037 (2017) · published 9 December 2017

doi: 10.21468/SciPostPhys.3.6.037
pdf
Submissions/Reports

Abstract

We consider the braid group representation which describes the non-abelian braiding statistics of the spin $1/2$ particle world lines of an SU(2)$_4$ Chern-Simons theory. Up to an abelian phase, this is the same as the non-Abelian statistics of the elementary quasiparticles of the $k=4$ Read-Rezayi quantum Hall state. We show that these braiding properties can be represented exactly using $\mathbb{Z}_3$ parafermion operators.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.3.6.037
TI  - How SU(2)$_4$ Anyons are Z$_3$ Parafermions
PY  - 2017/12/09
UR  - https://scipost.org/SciPostPhys.3.6.037
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 3
IS  - 6
SP  - 037
A1  - Fern, Richard
AU  - Kombe, Johannes
AU  - Simon, Steven
AB  - We consider the braid group representation which describes the non-abelian braiding statistics of the spin $1/2$ particle world lines of an SU(2)$_4$ Chern-Simons theory. Up to an abelian phase, this is the same as the non-Abelian statistics of the elementary quasiparticles of the $k=4$ Read-Rezayi quantum Hall state. We show that these braiding properties can be represented exactly using $\mathbb{Z}_3$ parafermion operators.
ER  -

@Article{10.21468/SciPostPhys.3.6.037,
	title={{How SU(2)$_4$ Anyons are Z$_3$ Parafermions}},
	author={Richard Fern and Johannes Kombe and Steven H. Simon},
	journal={SciPost Phys.},
	volume={3},
	pages={037},
	year={2017},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.3.6.037},
	url={https://scipost.org/10.21468/SciPostPhys.3.6.037},
}

Cited by 4

Ontology / Topics

See full Ontology or Topics database.

Anyons Braiding/braid group Chern-Simons theory Non-abelian statistics Parafermions Quasiparticles Read-Rezayi quantum Hall state

Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.

¹ Richard Fern,
² Johannes Kombe,
¹ Steven Simon

Funder for the research work leading to this publication

Engineering and Physical Sciences Research Council [EPSRC]