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 $\nu =8/3$.

• Received 30 May 2010

DOI:https://doi.org/10.1103/PhysRevLett.105.216804