Synthetic non-Abelian statistics by Abelian anyon condensation
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You-2013-Synthetic non-Abelian statistics.pdf
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3.39 MB
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Author(s)
You, Yi-Zhuang
Jian, Chao-Ming
Wen, Xiao-Gang
Date Issued
January 2013
Journal
Physical Review B
Publisher
American Physical Society
Citation
You, Yi-Zhuang, Chao-Ming Jian, and Xiao-Gang Wen. “Synthetic Non-Abelian Statistics by Abelian Anyon Condensation.” Phys. Rev. B 87, no. 4 (January 2013). © 2013 American Physical Society
Version
Final published version
Abstract
Topological degeneracy is the degeneracy of the ground states in a many-body system in the large-system-size limit. Topological degeneracy cannot be lifted by any local perturbation of the Hamiltonian. The topological degeneracies on closed manifolds have been used to discover/define topological order in many-body systems, which contain excitations with fractional statistics. In this paper, we study a new type of topological degeneracy induced by condensing anyons along a line in two-dimensional topological ordered states. Such topological degeneracy can be viewed as carried by each end of the line defect, which is a generalization of Majorana zero modes. The topological degeneracy can be used as a quantum memory. The ends of line defects carry projective non-Abelian statistics even though they are produced by the condensation of Abelian anyons, and braiding them allows us to perform fault tolerant quantum computations.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
http://dx.doi.org/10.1103/PhysRevB.87.045106
