Bosonization for fermions and parafermions
Physics and Materials Science Research Unit, University of Luxembourg,
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Received in final form: 26 July 2019
Published online: 14 February 2020
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.
© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature, 2020