Continuous Topological Phase Transitions in Non-Abelian Quantum Hall States

Abstract: Topological phases of matter cannot be characterized by any pattern of symmetry-breaking, and as a result, describing phase transitions between them is a significant theoretical challenge. In the case of non-Abelian phases, there are only a few examples of phase transitions that are theoretically understood. In this talk I will describe a possible continuous quantum phase transition from a (p,p,p-3) bilayer fractional quantum Hall (FQH) state to the Z₄ parafermion non-Abelian state, driven by increasing interlayer tunneling and/or interlayer repulsion. Previously used methods have failed because the transition from the (p,p,p-3) state appears to be driven by the condensation of anyons. After presenting a recently developed effective field theory for the Z₄ parafermion state, I will explain how it can be used, along with other methods, to shed light on the nature of this transition.