# 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 orbifold FQH states, of which the Z{sub 4} parafermion (Read-Rezayi) state is a special case. This provides an example in which Z{sub 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.

- Authors:

- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

- Publication Date:

- OSTI Identifier:
- 21596867

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. B, Condensed Matter and Materials Physics

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 11; Other Information: DOI: 10.1103/PhysRevB.84.115121; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1098-0121

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; GAUGE INVARIANCE; HAMILTONIANS; LAYERS; PHASE DIAGRAMS; PHASE TRANSFORMATIONS; QUANTUM MECHANICS; QUANTUM WELLS; TOPOLOGY; TUNNEL EFFECT; WAVE FUNCTIONS; DIAGRAMS; FUNCTIONS; INFORMATION; INVARIANCE PRINCIPLES; MATHEMATICAL OPERATORS; MATHEMATICS; MECHANICS; NANOSTRUCTURES; QUANTUM OPERATORS

### Citation Formats

```
Barkeshli, Maissam, and Wen Xiaogang.
```*Bilayer quantum Hall phase transitions and the orbifold non-Abelian fractional quantum Hall states*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVB.84.115121.

```
Barkeshli, Maissam, & Wen Xiaogang.
```*Bilayer quantum Hall phase transitions and the orbifold non-Abelian fractional quantum Hall states*. United States. doi:10.1103/PHYSREVB.84.115121.

```
Barkeshli, Maissam, and Wen Xiaogang. Thu .
"Bilayer quantum Hall phase transitions and the orbifold non-Abelian fractional quantum Hall states". United States. doi:10.1103/PHYSREVB.84.115121.
```

```
@article{osti_21596867,
```

title = {Bilayer quantum Hall phase transitions and the orbifold non-Abelian fractional quantum Hall states},

author = {Barkeshli, Maissam and Wen Xiaogang},

abstractNote = {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{sub 4} parafermion (Read-Rezayi) state is a special case. This provides an example in which Z{sub 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.},

doi = {10.1103/PHYSREVB.84.115121},

journal = {Physical Review. B, Condensed Matter and Materials Physics},

issn = {1098-0121},

number = 11,

volume = 84,

place = {United States},

year = {2011},

month = {9}

}