Quantum Double D(Z₂)

Kitaev's toric code lives on a 2D square lattice. Place electric (e), magnetic (m), and fermionic (ε=e×m) anyons. Drag one around another to observe the braiding phase. Fuse anyons by dropping them on each other.

Anyon Selector

Click grid to place. Click existing anyon to remove. Drag to move.
Place anyons on the lattice...

Fusion Table (D(Z₂))

×1emε
11emε
ee1εm
mmε1e
εεme1
Topological spins:
h(1)=0 (boson) | h(e)=0 (boson)
h(m)=0 (boson) | h(ε)=½ (fermion)

Braiding phases (e around m):
e↺m → phase π (mutual semion)
ε↺ε → phase -1 (self-statistics)
e↺e = m↺m → phase 1 (trivial)
Braiding log will appear here...