|
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, fractional quantum Hall states, and proposals for topological quantum computation. In this talk I will review some of the rich physics that arises in systems of *interacting* non-Abelian anyons. Topics include the topological protection of gapless ground states, unconventional phase transitions in one and two space dimensions and analogies to conventional spin systems. I will discuss both numerical and exact analytical results. |
|