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.