An integrable model with parafermion zero energy modes

Abstract

Parafermion zero energy modes are a vital element of fault-tolerant topological quantum computation. Although it is believed that such modes form on the border between topological and normal phases, this has been demonstrated only for Z${}_2$ (Majorana) and Z${}_3$ parafermions. I consider an integrable model where such demonstration is possible for Z${}_N$ parafermions with any $N$. The procedure is easely generalizable for more complicated symmetry groups.

4 pages

References in corpus (14)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• Measurement-Only Topological Quantum Computation
• Free parafermions
• Anyonic quantum spin chains: Spin-1 generalizations and topological stability
• Collective states of interacting Fibonacci anyons
• Solution of the Multichannel Coqblin-Schrieffer Impurity Model and Application to Multi-Level systems
• Thermodynamic Bethe Ansatz of the Homogeneous Sine-Gordon models
• A new set of exact form factors
• The Toulose limit of the Multi-Channel Kondo model.
• The $D(D_3)$-anyon chain: integrable boundary conditions and excitation spectra
• Riding a wild horse: Majorana fermions interacting with solitons of fast bosonic fields

Cited by in corpus (17)

• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• Non-Abelian parafermions in time-reversal invariant interacting helical systems
• Ground state degeneracy of non-Abelian topological phases from coupled wires
• Anyonic Topological Order in Twisted Equivariant Differential (TED) K-Theory
• Fibonacci anyon excitations of one-dimensional dipolar lattice bosons
• ${\mathbf{Z}}_n$ clock models and chains of $so(n{)}_2$ non-Abelian anyons: symmetries, integrable points and low energy properties
• Parafermion stabilizer codes
• Dynamical topological excitations in parafermion chains
• Pfaffian-like ground states for bosonic atoms and molecules in one-dimensional optical lattices
• Chiral topologically ordered insulating phases in arrays of interacting integer quantum Hall islands
• Interplay between intrinsic and emergent topological protection on interacting helical modes
• Anomalous Quantum Information Scrambling for ${\mathbb{Z}}_3$ Parafermion Chains
• Strong zero modes from geometric chirality in quasi-one-dimensional Mott insulators
• Signatures of non-Abelian anyons in the thermodynamics of an interacting fermion model
• Fibonacci topological phase in arrays of anyonic chains
• Condensates of interacting non-Abelian $SO(5{)}_{N_f}$ anyons
• Condensation of non-Abelian $SU(3{)}_{N_f}$ anyons in a one-dimensional fermion model