Non-Abelian FQH states and their phase transition

Xiao-Gang Wen, MIT

Boson condensation is not only a striking macroscopic quantum phenomenon, it also lays the foundation for our traditional theory of phases and phase transitions. In this talk, we discuss a generalization of boson condensation -- anyon condensation, which can describe a new class of continuous quantum phase transitions between, say, non-Abelian fractional quantum Hall (FQH) states. As an example, we study a possible quantum phase transition from a (p,p,p-3) bilayer FQH state to a Z₄ parafermion non-Abelian FQH state, driven by increasing interlayer tunneling and/or interlayer repulsion. We predict that the transition is a continuous transition in the 3D Ising class. The critical point is described by a Z₂ gauged Ginzburg-Landau theory.