  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. In this paper, we describe a simple fermionic version of
the toric code model to illustrate many salient features of fermionic exactly
soluble models and fermionic topologically ordered states.
