Bilayer quantum Hall phase transitions and the orbifold non-Abelian fractional quantum Hall states

We study continuous quantum phase transitions that can occur in bilayer fractional quantum Hall (FQH) systems as the interlayer tunneling and interlayer repulsion are tuned. We introduce a slave-particle gauge theory description of a series of continuous transitions from the $(ppq)$ Abelian bilayer states to a set of non-Abelian FQH states, which we dub orbifold FQH states, of which the Z₄ parafermion (Read-Rezayi) state is a special case. This provides an example in which Z₂ electron fractionalization leads to non-Abelian topological phases. The naive ``ideal'' wave functions and ideal Hamiltonians associated with these orbifold states do not in general correspond to incompressible phases but, instead, lie at a nearby critical point. We discuss this unusual situation from the perspective of the pattern-of-zeros/vertex algebra frameworks and discuss implications for the conceptual foundations of these approaches. Due to the proximity in the phase diagram of these non-Abelian states to the $(ppq)$ bilayer states, they may be experimentally relevant, both as candidates for describing the plateaus in single-layer systems at filling fractions $8/3$ and $12/5$ and as a way to tune to non-Abelian states in double-layer or wide quantum wells.