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

• Main Authors: Barkeshli, Maissam (Contributor), Wen, Xiao-Gang (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Physics (Contributor)
• Format: Article
• Language: English
• Published: American Physical Society (APS), 2012-02-17T17:45:08Z.
• Subjects: Article
• Online Access: Get fulltext

 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 Z[subscript 4] parafermion (Read-Rezayi) state is a special case. This provides an example in which Z[subscript 2] 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.