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.

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

References in corpus (16)

• Non-Abelian Anyons and Topological Quantum Computation
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Introduction to topological superconductivity and Majorana fermions
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Genons, twist defects, and projective non-Abelian braiding statistics
• Time-Reversal-Invariant $Z_4$ Fractional Josephson Effect
• Kramers Pairs of Majorana Fermions and Parafermions in Fractional Topological Insulators
• Quantum Hall effect in graphene with superconducting electrodes
• Non-Abelian parafermions in time-reversal invariant interacting helical systems
• Parafermionic conformal field theory on the lattice
• ${\mathbb{Z}}_4$ Parafermions in an interacting quantum spin Hall Josephson junction coupled to an impurity spin
• Pretopological fractional excitations in the two-leg flux ladder
• Dynamic response functions and helical gaps in interacting Rashba nanowires with and without magnetic fields
• Missing Shapiro steps and the $8\pi$-periodic Josephson effect in interacting helical electron systems
• Generalized parafermions and non-local Josephson effect in multi-layer systems
• Spin-orbit coupling in quasi-one-dimensional Wigner crystals

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