Synthetic Topological Degeneracy by Anyon Condensation
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.
Keywords
Cite
@article{arxiv.1208.4109,
title = {Synthetic Topological Degeneracy by Anyon Condensation},
author = {Yi-Zhuang You and Chao-Ming Jian and Xiao-Gang Wen},
journal= {arXiv preprint arXiv:1208.4109},
year = {2015}
}
Comments
4 pages + references + 3 pages of supplementary material, 2 figures. reference updated