Beyond the Search for Majorana

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The search for Majorana zero-modes in condensed matter
system has attract increasing research interests recently. Looking for Majorna
zero-mode is actually looking for topologically protected ground state
degeneracy. 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 talk, I will present our recent
work on new types 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 ends of line-defects carry projective non-Abelian
statistics even though they are produced by condensation of Abelian anyons, and
braiding them allow us to perform fault tolerant quantum computations.