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

TL;DR

This paper explores continuous phase transitions in bilayer fractional quantum Hall systems, introducing a gauge theory framework for non-Abelian orbifold states, which are potentially experimentally accessible and conceptually significant.

Contribution

It presents a slave-particle gauge theory description of continuous transitions from Abelian to non-Abelian FQH states, specifically the orbifold states, including the Z4 parafermion state.

Findings

Orbifold FQH states include the Z4 parafermion state.

Ideal wave functions for these states are often at critical points, not incompressible phases.

Non-Abelian states are close to Abelian bilayer states in the phase diagram, relevant for experiments.

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.