Anyon Condensation and Continuous Topological Phase Transitions in Non-Abelian Fractional Quantum Hall States

We find a series of possible continuous quantum phase transitions between fractional quantum Hall states at the same filling fraction in two-component quantum Hall systems. These can be driven by tuning the interlayer tunneling and/or interlayer repulsion. One side of the transition is the Halperin (p, p, p - 3) Abelian two-component state, while the other side is the non-Abelian Z(4) parafermion (Read-Rezayi) state. We predict that the transition is a continuous transition in the 3D Ising class. The critical point is described by a Z(2) gauged Ginzburg-Landau theory. These results have implications for experiments on two-component systems at nu = 2/3 and single-component systems at nu = 8/3.