Bosonization for fermions and parafermions

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.

arXiv commentInvited review for the EPJ Special Topics issue on "New directions in the physics of one-dimensional electron systems". Comments are welcome!

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Cited by in corpus (10)

• Majorana nanowires for topological quantum computation
• Majorana bound states in semiconducting nanostructures
• Current correlations of Cooper-pair tunneling into a quantum Hall system
• Anomalous periodicity and parafermion hybridization in superconducting qubits
• Altermagnet-Superconductor Heterostructure: a Scalable Platform for Braiding of Majorana Modes
• Generalized Josephson effect with arbitrary periodicity in quantum magnets
• Overlap of parafermionic zero modes at a finite distance
• Phases of Quasi-One-Dimensional Fractional Quantum (Anomalous) Hall - Superconductor Heterostructures
• Bosonization in $R$-paraparticle Luttinger models
• Noninteracting tight-binding models for Fock parafermions