Non-Abelian Three-Loop Braiding Statistics for 3D Fermionic Topological Phases

Understand

Fractional statistics is one of the most intriguing features of topological phases in 2D.

• In particular, the so-called non-Abelian statistics plays a crucial role towards realizing universal topological quantum computation.
• Recently, the study of topological phases has been extended to 3D and it has been proposed that loop-like extensive objects can also carry fractional statistics.
• In this work, we systematically study the so-called three-loop braiding statistics for loop-like excitations for 3D fermionic topological phases.