Lattice Model for Fermionic Toric Code

Understand

The Z_2 topological order in Z_2 spin liquid and in exactly soluble Kitaev toric code model is the simplest topological order for 2+1D bosonic systems.

• More general 2+1D bosonic topologically ordered states can be constructed via exact soluble string-net models.
• However, the most important topologically ordered phases of matter are arguably the fermionic fractional quantum Hall states.
• Topological phases of matter for fermion systems are strictly richer than their bosonic counterparts because locality has different meanings for the two kinds of systems.