# Bosonization for fermions and parafermions

## TL;DR

This paper reviews the theoretical framework for understanding parafermions in one-dimensional systems, emphasizing bosonization and renormalization-group methods to analyze their properties and potential for quantum computation.

## Contribution

It provides a pedagogical introduction to parafermion bound states, detailing the application of bosonization and renormalization-group techniques for their study.

## Key findings

- Introduction of bosonization as a tool for parafermion analysis
- Application of renormalization-group methods to parafermions
- Clarification of parafermions' role in topological quantum computation

## 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.