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

TL;DR

This paper uses boundary conformal field theory to analyze edge quasiparticle tunneling in non-Abelian topological states, revealing how boundary condition flows correspond to tunneling phenomena and illustrating these concepts with quantum Hall and Ising models.

Contribution

It introduces a novel framework connecting boundary conformal field theory with quasiparticle tunneling in non-Abelian states, providing detailed models and physical interpretations.

Findings

Tunneling causes flow between boundary conditions in conformal models.

Edge tunneling can split the system into separate parts.

The framework applies to quantum Hall states and Fibonacci anyons.

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.