U(1)xU(1)xZ{sub 2} Chern-Simons theory and Z{sub 4} parafermion fractional quantum Hall states

doi:https://doi.org/10.1103/PHYSREVB.81.045323

Title: U(1)xU(1)xZ{sub 2} Chern-Simons theory and Z{sub 4} parafermion fractional quantum Hall states

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Abstract

We study U(1)xU(1)xZ{sub 2} Chern-Simons theory with integral coupling constants (k,l) and its relation to certain non-Abelian fractional quantum Hall (FQH) states. For the U(1)xU(1)xZ{sub 2} Chern-Simons 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} Chern-Simons theory carry non-Abelian 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} Chern-Simons theory is the low-energy effective theory for the Z{sub 4} parafermion (Read-Rezayi) fractional quantum Hall states, which occur at filling fraction nu=(2/2k-3). The U(1)xU(1)xZ{sub 2} theory is more useful than an alternative SU(2){sub 4}xU(1)/U(1) Chern-Simons 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 two-component to single-component 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:

Barkeshli, Maissam; Xiaogang, Wen ^[1]

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

Publication Date:: 2010-01-15

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 1098-0121

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; ENERGY-LEVEL TRANSITIONS; FERMIONS; FIELD THEORIES; INFORMATION; LEPTONS; MATHEMATICAL SPACE; MATHEMATICS; SPACE

Citation Formats


                    Barkeshli, Maissam, and Xiaogang, Wen. U(1)xU(1)xZ{sub 2} Chern-Simons theory and Z{sub 4} parafermion fractional quantum Hall states.  United States: N. p., 2010. 
        Web.  doi:10.1103/PHYSREVB.81.045323.

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                    Barkeshli, Maissam, & Xiaogang, Wen. U(1)xU(1)xZ{sub 2} Chern-Simons theory and Z{sub 4} parafermion fractional quantum Hall states.  United States.  https://doi.org/10.1103/PHYSREVB.81.045323

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                    Barkeshli, Maissam, and Xiaogang, Wen. Fri .  
        "U(1)xU(1)xZ{sub 2} Chern-Simons theory and Z{sub 4} parafermion fractional quantum Hall states".  United States.  https://doi.org/10.1103/PHYSREVB.81.045323.

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@article{osti_21366669,

  title        = {U(1)xU(1)xZ{sub 2} Chern-Simons 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} Chern-Simons theory with integral coupling constants (k,l) and its relation to certain non-Abelian fractional quantum Hall (FQH) states. For the U(1)xU(1)xZ{sub 2} Chern-Simons 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} Chern-Simons theory carry non-Abelian 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} Chern-Simons theory is the low-energy effective theory for the Z{sub 4} parafermion (Read-Rezayi) fractional quantum Hall states, which occur at filling fraction nu=(2/2k-3). The U(1)xU(1)xZ{sub 2} theory is more useful than an alternative SU(2){sub 4}xU(1)/U(1) Chern-Simons 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 two-component to single-component 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         = {1098-0121},

  number       = 4,

  volume       = 81,

  place        = {United States},

  year         = {2010},

  month        = {1}

}

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