Two-dimensional quantum liquids from interacting non-Abelian anyons

Abstract

A set of localized, non-Abelian anyons—such as vortices in a px+ipy superconductor or quasiholes in certain quantum Hall states—gives rise to a macroscopic degeneracy. Such a degeneracy is split in the presence of interactions between the anyons. Here, we show that in two spatial dimensions this splitting selects a unique collective state as ground state of the interacting many-body system. This collective state can be a novel gapped quantum liquid nucleated inside the original parent liquid (of which the anyons are excitations). This physics is of relevance for any quantum Hall plateau realizing a non-Abelian quantum Hall state when moving off the center of the plateau.