Spin chains, defects, and quantum wires for the quantum-double edge

Understand

Non-Abelian defects that bind Majorana or parafermion zero modes are prominent in several topological quantum computation schemes.

• Underpinning their established understanding is the quantum Ising spin chain, which can be recast as a fermionic model or viewed as a standalone effective theory for the surface-code edge -- both of which harbor non-Abelian defects.
• We generalize these notions by deriving an effective Ising-like spin chain describing the edge of quantum-double topological order.
• Relating Majorana and parafermion modes to anyonic strings, we introduce quantum-double generalizations of non-Abelian defects.