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

Abstract: 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 the 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 fraction 8/3 and 12/5, and as a way to tune to non-Abelian states in double-layer or wide quantum wells.