Topological Order with a Twist: Ising Anyons from an Abelian Model

Understand

Anyon models can be symmetric under some permutations of their topological charges.

• One can then conceive topological defects that, under monodromy, transform anyons according to a symmetry.
• We study the realization of such defects in the toric code model, showing that a process where defects are braided and fused has the same outcome as if they were Ising anyons.
• These ideas can also be applied in the context of topological codes.