Non-Abelian anyons: when Ising meets Fibonacci

We analyze the edge lying on the interface of two non-Abelian quantum Hall states: the Moore-Read spin-polarized state at filling factor 1/2, supporting Ising anyons, and the non-Abelian spin-singlet state at filling factor 4/7, supporting Fibonacci anyons. We find that the neutral sector of the edge is described by a minimal model with central charge 7/10. We explore the role of the edge as a mediator between regions of different quantum statistics.