Non-Abelian anyons: when Ising meets Fibonacci

Abstract

We consider an interface between two non-Abelian quantum Hall states: the Moore-Read state, supporting anyons of Ising type, and the k=2 NASS (non-Abelian spin-singlet) state, supporting anyons of Fibonacci type. It is shown that the interface supports neutral excitations described by a 1+1 dimensional conformal field theory with central charge c=7/10. We discuss effects of the mismatch of the quantum statistical properties of the quasi-holes between the two sides, as reflected by the interface theory.

As published in PRL

References in corpus (7)

• Non-Abelian Anyons and Topological Quantum Computation
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Condensate induced transitions between topologically ordered phases
• Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
• Wavefunctions for topological quantum registers
• Experimental signatures of non-Abelian statistics in clustered quantum Hall states

Cited by in corpus (33)

• Interacting Fibonacci anyons in a Rydberg gas
• Diagrammatics for Bose condensation in anyon theories
• Boson Condensation in Topologically Ordered Quantum Liquids
• Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
• Anyon Condensation and Continuous Topological Phase Transitions in Non-Abelian Fractional Quantum Hall States
• Two-dimensional quantum liquids from interacting non-Abelian anyons
• Interacting Majorana Fermions
• Fibonacci Topological Superconductor
• Microscopic Study of the Halperin - Laughlin Interface through Matrix Product States
• Model States for a Class of Chiral Topological Order Interfaces
• Topological Interface between Pfaffian and anti-Pfaffian Order in $\nu =5/2$ Quantum Hall Effect
• Spin-Singlet Quantum Hall States and Jack Polynomials with a Prescribed Symmetry
• The modular S-matrix as order parameter for topological phase transitions
• Condensate-induced transitions and critical spin chains
• A general approach to quantum Hall hierarchies
• Interface and Phase Transition between Moore-Read and Halperin 331 Fractional Quantum Hall States: Realization of Chiral Majorana Fermion
• One-dimensional itinerant interacting non-Abelian anyons
• Exact solution of the $D_3$ non-Abelian anyon chain
• Out of Equilibrium Majoranas in Interacting Kitaev Chains
• Simple analog of the black-hole information paradox in quantum Hall interfaces
• Model wavefunctions for interfaces between lattice Laughlin states
• Model wavefunctions for an interface between lattice Laughlin and Moore-Read states
• Non-Abelian $SU(3{)}_k$ anyons: inversion identities for higher rank face models
• Integrability in anyonic quantum spin chains via a composite height model
• Dynamics of Quantum Hall Interfaces
• Hetero-Orbital Two-Component Fractional Quantum Hall States in Bilayer Graphene
• Universal charge conductance at Abelian--non-Abelian quantum Hall interfaces
• Spin-singlet Gaffnian wave function for fractional quantum Hall systems
• Collective states of interacting $D(D_3)$ non-Abelian anyons
• From $G_2$ to $SO(8)$: Emergence and reminiscence of supersymmetry and triality
• Bosonic Halperin fractional quantum Hall effect at filling factor $\nu =2/5$
• Signatures of non-Abelian anyons in the thermodynamics of an interacting fermion model
• Local height probabilities in a composite Andrews-Baxter-Forrester model