Non-Abelian Anyons: When Ising Meets Fibonacci

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