U(1)xU(1)xZ{sub 2} ChernSimons theory and Z{sub 4} parafermion fractional quantum Hall states
Abstract
We study U(1)xU(1)xZ{sub 2} ChernSimons theory with integral coupling constants (k,l) and its relation to certain nonAbelian fractional quantum Hall (FQH) states. For the U(1)xU(1)xZ{sub 2} ChernSimons theory, we show how to compute the dimension of its Hilbert space on genus g surfaces and how this yields the quantum dimensions of topologically distinct excitations. We find that Z{sub 2} vortices in the U(1)xU(1)xZ{sub 2} ChernSimons theory carry nonAbelian statistics and we show how to compute the dimension of the Hilbert space in the presence of n pairs of Z{sub 2} vortices on a sphere. These results allow us to show that l=3 U(1)xU(1)xZ{sub 2} ChernSimons theory is the lowenergy effective theory for the Z{sub 4} parafermion (ReadRezayi) fractional quantum Hall states, which occur at filling fraction nu=(2/2k3). The U(1)xU(1)xZ{sub 2} theory is more useful than an alternative SU(2){sub 4}xU(1)/U(1) ChernSimons theory because the fields are more closely related to physical degrees of freedom of the electron fluid and to an Abelian bilayer phase on the other side of a twocomponent to singlecomponent quantum phase transition. We discuss the possibility of using this theory to understand further phase transitions in FQH systems, especially the nu=2/3 phase diagram.
 Authors:

 Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
 Publication Date:
 OSTI Identifier:
 21366669
 Resource Type:
 Journal Article
 Journal Name:
 Physical Review. B, Condensed Matter and Materials Physics
 Additional Journal Information:
 Journal Volume: 81; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevB.81.045323; (c) 2010 The American Physical Society; Journal ID: ISSN 10980121
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COUPLING CONSTANTS; DEGREES OF FREEDOM; ELECTRONS; EXCITATION; FLUIDS; HILBERT SPACE; LAYERS; PHASE DIAGRAMS; PHASE TRANSFORMATIONS; QUANTUM FIELD THEORY; STATISTICS; SURFACES; VORTICES; BANACH SPACE; DIAGRAMS; ELEMENTARY PARTICLES; ENERGYLEVEL TRANSITIONS; FERMIONS; FIELD THEORIES; INFORMATION; LEPTONS; MATHEMATICAL SPACE; MATHEMATICS; SPACE
Citation Formats
Barkeshli, Maissam, and Xiaogang, Wen. U(1)xU(1)xZ{sub 2} ChernSimons theory and Z{sub 4} parafermion fractional quantum Hall states. United States: N. p., 2010.
Web. doi:10.1103/PHYSREVB.81.045323.
Barkeshli, Maissam, & Xiaogang, Wen. U(1)xU(1)xZ{sub 2} ChernSimons theory and Z{sub 4} parafermion fractional quantum Hall states. United States. https://doi.org/10.1103/PHYSREVB.81.045323
Barkeshli, Maissam, and Xiaogang, Wen. Fri .
"U(1)xU(1)xZ{sub 2} ChernSimons theory and Z{sub 4} parafermion fractional quantum Hall states". United States. https://doi.org/10.1103/PHYSREVB.81.045323.
@article{osti_21366669,
title = {U(1)xU(1)xZ{sub 2} ChernSimons theory and Z{sub 4} parafermion fractional quantum Hall states},
author = {Barkeshli, Maissam and Xiaogang, Wen},
abstractNote = {We study U(1)xU(1)xZ{sub 2} ChernSimons theory with integral coupling constants (k,l) and its relation to certain nonAbelian fractional quantum Hall (FQH) states. For the U(1)xU(1)xZ{sub 2} ChernSimons theory, we show how to compute the dimension of its Hilbert space on genus g surfaces and how this yields the quantum dimensions of topologically distinct excitations. We find that Z{sub 2} vortices in the U(1)xU(1)xZ{sub 2} ChernSimons theory carry nonAbelian statistics and we show how to compute the dimension of the Hilbert space in the presence of n pairs of Z{sub 2} vortices on a sphere. These results allow us to show that l=3 U(1)xU(1)xZ{sub 2} ChernSimons theory is the lowenergy effective theory for the Z{sub 4} parafermion (ReadRezayi) fractional quantum Hall states, which occur at filling fraction nu=(2/2k3). The U(1)xU(1)xZ{sub 2} theory is more useful than an alternative SU(2){sub 4}xU(1)/U(1) ChernSimons theory because the fields are more closely related to physical degrees of freedom of the electron fluid and to an Abelian bilayer phase on the other side of a twocomponent to singlecomponent quantum phase transition. We discuss the possibility of using this theory to understand further phase transitions in FQH systems, especially the nu=2/3 phase diagram.},
doi = {10.1103/PHYSREVB.81.045323},
url = {https://www.osti.gov/biblio/21366669},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
issn = {10980121},
number = 4,
volume = 81,
place = {United States},
year = {2010},
month = {1}
}