  A spin 1/2 system on a honeycomb lattice is studied. The interactions between
nearest neighbors are of XX, YY or ZZ type, depending on the direction of the
link; different types of interactions may differ in strength. The model is
solved exactly by a reduction to free fermions in a static $\mathbb{Z}_{2}$
gauge field. A phase diagram in the parameter space is obtained. One of the
phases has an energy gap and carries excitations that are Abelian anyons. The
other phase is gapless, but acquires a gap in the presence of magnetic field.
In the latter case excitations are non-Abelian anyons whose braiding rules
coincide with those of conformal blocks for the Ising model. We also consider a
general theory of free fermions with a gapped spectrum, which is characterized
by a spectral Chern number $\nu$. The Abelian and non-Abelian phases of the
original model correspond to $\nu=0$ and $\nu=\pm 1$, respectively. The anyonic
properties of excitation depend on $\nu\bmod 16$, whereas $\nu$ itself governs
edge thermal transport. The paper also provides mathematical background on
anyons as well as an elementary theory of Chern number for quasidiagonal
matrices.
