Interacting anyons in topological quantum liquids

Simon Trebst, Microsoft Research / Station Q

Two-dimensional topological quantum liquids harbor exotic quasiparticle excitations which due to their unusual exchange statistics are referred to as anyons. Interchanging two anyons may result in not only a fractional exchange phase, but may also give rise to a unitary rotation of the original wave function in a degenerate ground-state manifold. This latter case of non-Abelian statistics is being studied in a variety of contexts such as unconventional px + ipy superconductors, rotating Bose-Einstein condensates, fractional quantum Hall states, and proposals for topological quantum computation.

Interactions mediated by quasiparticle tunneling split the degenerate space of states formed by a set of localized, non-Abelian anyons. In this talk I will discuss how this splitting selects a unique collective state as the ground state of the interacting, many-anyon system. The formation of this collective state can be interpreted as the nucleation of a novel quantum liquid inside the original topological liquid. I will outline how this physics is at play for non-Abelian quantum Hall liquids off the center of the quantum Hall plateau and discuss possible experimental signatures.