Phase-shift Instanton Approach to Tunneling Duality in Read–Rezayi State

Abstract

We study the duality between quasi-particle and electron tunneling in point-contact geometries of fractional quantum Hall states. To treat non-Abelian edge operators, we introduce a “phase-shift instanton” that incorporates phase factors from primary fields into the instanton gas framework. Using this method, we reformulate the Moore–Read duality and obtain an explicit dual description for the k = 3 Read–Rezayi state. Our results clarify how quasi-particle tunneling produces characteristic phase shifts in instantons and how these shifts map strong quasi-particle tunneling to weak electron tunneling. Based on this dual description, we analytically evaluate the non-linear differential conductance in the strong-coupling limit. We reveal that, due to the physical requirement that the tunneling particle across the bulk must be a true fermion, the transport behavior universally converges to a G ∝ V 4 scaling for both the Moore–Read and Read–Rezayi states. This universal transport signature highlights a fundamental topological constraint underlying non-Abelian fractional quantum Hall edges.