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Twist Defects in Topological Systems with Anyonic Symmetries

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Twist defects are point-like objects that support robust non-local
storage of quantum information and non-abelian unitary operations.
Unlike quantum deconfined anyonic excitations, they rely on symmetry
rather than a non-abelian topological order. Zero energy Majorana bound
states can arise at lattice defects, such as disclinations and
dislocations, in a topological crystalline superconductor. More general
parafermion bound state can appear as twist defects in a topological
phase with an anyonic symmetry, such as a bilayer fractional quantum
Hall state and the Kitaev toric code. They are however fundamentally
different from quantum anyonic excitations in a true topological phase.
This is demonstrated by their unconventional exchange and braiding
behavior, which is characterized by a modified spin statistics theorem
and modular invariance.