Formation of novel topological liquids in non-Abelian quantum Hall states with a finite density of interacting anyons

We discuss the nucleation of novel topological liquids within a `parent' non-Abelian quantum Hall state that arises from a macroscopic occupation of the parent liquid with interacting anyons. The edge states between the `nucleated' and the `parent' liquids are neutral, and correspond precisely to the gapless modes of chains of interacting anyons. Exploring the collective states of anyonic spin chains is thus, at the same time, a tool to systematically study topological phases which can occur inside non-Abelian quantum Hall liquids due to population of such liquids with a finite density of interacting non-Abelian anyons. We discuss several examples including the interface between the Moore-Read and Read-Rezayi quantum Hall states.