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Title: 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:
;  [1]
  1. 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}
}