Eur. Phys. J. Special Topics 229, 621–636 (2020)
https://doi.org/10.1140/epjst/e2019-900112-y

Review

Bosonization for fermions and parafermions

Physics and Materials Science Research Unit, University of Luxembourg, 1511 Luxembourg, Luxembourg

^a e-mail: thomas.schmidt@uni.lu

Received: 17 June 2019
Received in final form: 26 July 2019
Published online: 14 February 2020

Abstract

Parafermions are fractional excitations which can be regarded as generalizations of Majorana bound states, but in contrast to the latter they require electron-electron interactions. Compared to Majorana bound states, they offer richer non-Abelian braiding statistics, and have thus been proposed as building blocks for topologically protected universal quantum computation. In this review, we provide a pedagogical introduction to the field of parafermion bound states in one-dimensional systems. We present the necessary theoretical tools for their study, in particular bosonization and the renormalization-group technique, and show how those can be applied to study parafermions.