Mutual Chern-Simons theory for Z{sub 2} topological order

doi:https://doi.org/10.1103/PHYSREVB.78.155134

Title: Mutual Chern-Simons theory for Z{sub 2} topological order

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Abstract

We study several different Z{sub 2} topological ordered states in frustrated spin systems. The effective theories for those different Z{sub 2} topological orders all have the same form--a Z{sub 2} gauge theory which can also be written as a mutual U(1)xU(1) Chern-Simons theory. However, we find that the different Z{sub 2} topological orders are reflected in different projective realizations of lattice symmetry in the same effective mutual Chern-Simons theory. This result is obtained by comparing the ground-state degeneracy, the ground-state quantum numbers, the gapless edge state, and the projective symmetry group of quasiparticles calculated from the slave-particle theory and from the effective mutual Chern-Simons theories. Our study reveals intricate relations between topological order and symmetry.

Authors:

Supeng, Kou ^[1]; Levin, Michael ^[2]; Xiaogang, Wen ^[3]

Department of Physics, Beijing Normal University, Beijing 100875 (China)
Department of Physics, Harvard University, Cambridge, Massachusetts 02138 (United States)
Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

Publication Date:: 2008-10-15

OSTI Identifier:: 21192464

Resource Type:: Journal Article

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

Additional Journal Information:: Journal Volume: 78; Journal Issue: 15; Other Information: DOI: 10.1103/PhysRevB.78.155134; (c) 2008 The American Physical Society; 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; GROUND STATES; PARTICLES; QUANTUM NUMBERS; QUASI PARTICLES; SPIN; SYMMETRY; SYMMETRY GROUPS

Citation Formats


                    Supeng, Kou, Levin, Michael, and Xiaogang, Wen. Mutual Chern-Simons theory for Z{sub 2} topological order.  United States: N. p., 2008. 
        Web.  doi:10.1103/PHYSREVB.78.155134.

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                    Supeng, Kou, Levin, Michael, & Xiaogang, Wen. Mutual Chern-Simons theory for Z{sub 2} topological order.  United States.  https://doi.org/10.1103/PHYSREVB.78.155134

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                    Supeng, Kou, Levin, Michael, and Xiaogang, Wen. Wed .  
        "Mutual Chern-Simons theory for Z{sub 2} topological order".  United States.  https://doi.org/10.1103/PHYSREVB.78.155134.

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@article{osti_21192464,

  title        = {Mutual Chern-Simons theory for Z{sub 2} topological order},

  author       = {Supeng, Kou and Levin, Michael and Xiaogang, Wen},

  abstractNote = {We study several different Z{sub 2} topological ordered states in frustrated spin systems. The effective theories for those different Z{sub 2} topological orders all have the same form--a Z{sub 2} gauge theory which can also be written as a mutual U(1)xU(1) Chern-Simons theory. However, we find that the different Z{sub 2} topological orders are reflected in different projective realizations of lattice symmetry in the same effective mutual Chern-Simons theory. This result is obtained by comparing the ground-state degeneracy, the ground-state quantum numbers, the gapless edge state, and the projective symmetry group of quasiparticles calculated from the slave-particle theory and from the effective mutual Chern-Simons theories. Our study reveals intricate relations between topological order and symmetry.},

  doi          = {10.1103/PHYSREVB.78.155134},

  url          = {https://www.osti.gov/biblio/21192464},
  journal      = {Physical Review. B, Condensed Matter and Materials Physics},

  issn         = {1098-0121},

  number       = 15,

  volume       = 78,

  place        = {United States},

  year         = {2008},

  month        = {10}

}

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