Globally symmetric topological phase: from anyonic symmetry to twist defect

Understand

Topological phases in two dimensions support anyonic quasiparticle excitations that obey neither bosonic nor fermionic statistics.

• These anyon structures often carry global symmetries that relate distinct anyons with similar fusion and statistical properties.
• Anyonic symmetries associate topological defects or fluxes in topological phases.
• As the symmetries are global and static, these extrinsic defects are semiclassical objects that behave disparately from conventional quantum anyons.