Condensation of fractional excitons, non-Abelian states in double-layer quantum Hall systems and Z_4 parafermions

In this paper, we study a method to obtain non-Abelian FQH state through double-layer FQH states and fractional exciton condensation. In particular, we find that starting with the (330) double-layer state and then increasing the interlayer tunneling strength, we may obtain a single-layer non-Abelian FQH state S(330). We show that the S(330) state is actually the Z_4 parafermion Read-Rezayi state. We also calculate the edge excitation of the S(330) state.