PIRSA:13110078

Twist Defects in Topological Systems with Anyonic Symmetries

Teo, J. (2013). Twist Defects in Topological Systems with Anyonic Symmetries. Perimeter Institute. https://pirsa.org/13110078

Teo, Jeffrey. Twist Defects in Topological Systems with Anyonic Symmetries. Perimeter Institute, Nov. 08, 2013, https://pirsa.org/13110078 

          @misc{ pirsa_PIRSA:13110078,
            doi = {10.48660/13110078},
            url = {https://pirsa.org/13110078},
            author = {Teo, Jeffrey},
            keywords = {},
            language = {en},
            title = {Twist Defects in Topological Systems with Anyonic Symmetries},
            publisher = {Perimeter Institute},
            year = {2013},
            month = {nov},
            note = {PIRSA:13110078 see, \url{https://pirsa.org}}
          }

Jeffrey Teo University of Illinois Urbana-Champaign

DOI 10.48660/13110078
Collection
Talk Type Conference

Abstract

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.