Projective non-Abelian statistics of dislocation defects in a Z[subscript N] rotor model
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You-2012-Projective non-Abelian statistics of dislocation defects.pdf
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Author(s)
You, Yi-Zhuang
Wen, Xiao-Gang
Date Issued
October 2012
Journal
Physical Review B
Publisher
American Physical Society
Citation
You, Yi-Zhuang, and Xiao-Gang Wen. “Projective non-Abelian statistics of dislocation defects in a Z[subscript N] rotor model.” Physical Review B 86.16 (2012). © 2012 American Physical Society
Version
Final published version
Abstract
Non-Abelian statistics is a phenomenon of topologically protected non-Abelian geometric phases as we exchange quasiparticle excitations. Here we construct a Z[subscript N] rotor model that realizes a self-dual Z[subscript N] Abelian gauge theory. We find that lattice dislocation defects in the model produce topologically protected degeneracy. Even though dislocations are not quasiparticle excitations, they resemble non-Abelian anyons with quantum dimension √N. Exchanging dislocations can produce topologically protected projective non-Abelian geometric phases. Therefore, we discover a kind of (projective) non-Abelian anyon that appears as the dislocations in an Abelian Z[subscript N] rotor model. These types of non-Abelian anyons can be viewed as a generalization of the Majorana zero modes.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevB.86.161107
