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arXiv · 1208.4109

Synthetic Topological Degeneracy by Anyon Condensation

Yi-Zhuang You·Chao-Ming Jian·Xiao-Gang Wen
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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 2D 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, and braiding them allow us to perform fault tolerant quantum computations.

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Yi-Zhuang You, Chao-Ming Jian, Xiao-Gang Wen. 2012-08-24. Synthetic Topological Degeneracy by Anyon Condensation. https://doi.org/10.1103/physrevb.87.045106

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