Boundary Conformal Field Theory and Tunneling of Edge Quasiparticles in non-Abelian Topological States

Abstract

We explain how (perturbed) boundary conformal field theory allows us to understand the tunneling of edge quasiparticles in non-Abelian topological states. The coupling between a bulk non-Abelian quasiparticle and the edge is due to resonant tunneling to a zero mode on the quasiparticle, which causes the zero mode to hybridize with the edge. This can be reformulated as the flow from one conformally-invariant boundary condition to another in an associated critical statistical mechanical model. Tunneling from one edge to another at a point contact can split the system in two, either partially or completely. This can be reformulated in the critical statistical mechanical model as the flow from one type of defect line to another. We illustrate these two phenomena in detail in the context of the nu=5/2 quantum Hall state and the critical Ising model. We briefly discuss the case of Fibonacci anyons and conclude by explaining the general formulation and its physical interpretation.

References in corpus (12)

• 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
• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Observing Majorana Bound States in p-wave Superconductors Using Noise Measurements in Tunneling Experiments
• Topological Entanglement Entropy from the Holographic Partition Function
• Order parameter statistics in the critical quantum Ising chain
• Edge States and Interferometers in the Pfaffian and anti-Pfaffian States
• Dynamical Disentanglement across a Point Contact in a Non-Abelian Quantum Hall State
• Bulk-edge coupling in the non-abelian $\nu =5/2$ quantum Hall interferometer
• Quantum Hall States at $\nu =\frac{2}{k+2}$
• Prediction of the capacitance lineshape in two-channel quantum dots

Cited by in corpus (32)

• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• Topologically Protected Quantum State Transfer in a Chiral Spin Liquid
• Lifetime of almost strong edge-mode operators in one dimensional, interacting, symmetry protected topological phases
• Electrical probes of the non-Abelian spin liquid in Kitaev materials
• Emptiness formation probability, Toeplitz determinants, and conformal field theory
• Almost strong 0, π edge modes in clean, interacting 1D Floquet systems
• Partial Equilibration of the Anti-Pfaffian edge due to Majorana Disorder
• Defect flows in minimal models
• Non-Abelian Anyon Collider
• Odd-Even Crossover in a non-Abelian $\nu =5/2$ Interferometer
• Entanglement asymmetry in CFT and its relation to non-topological defects
• Realization of supersymmetry and its spontaneous breaking in quantum Hall edges
• Designer non-Abelian anyon platforms: from Majorana to Fibonacci
• Universal nonequilibrium signatures of Majorana zero modes in quench dynamics
• Defect loops in gauged Wess-Zumino-Witten models
• Integrable Kondo problems
• Partition Functions of Non-Abelian Quantum Hall States
• Thermal anyon interferometry in phonon-coupled Kitaev spin liquids
• Non-local conserved charges from defects in perturbed conformal field theory
• Parafermionic zero modes in ultracold bosonic systems
• Boundary deconfined quantum criticality at transitions between symmetry-protected topological chains
• Size Constraints on Majorana Beamsplitter Interferometer: Majorana Coupling and Surface-Bulk Scattering
• Exotic resonant level models in non-Abelian quantum Hall states coupled to quantum dots
• Spin correlation function in 2D statistical mechanics models with inhomogeneous line defects
• Conformal Defects from String Field Theory
• Topological strings linking with quasi-particle exchange in superconducting Dirac semimetals
• Non-Fermi Liquid Quantum Impurity Physics from non-Abelian Quantum Hall States
• Collective states of interacting $D(D_3)$ non-Abelian anyons
• Non-Abelian anyon statistics through AC conductance of a Majorana interferometer
• Defects and Perturbation
• Strongly Correlated Transport in Topological Y-Junction Devices
• Time-domain anyon interferometry in Kitaev honeycomb spin liquids and beyond