A family of two-dimensional (2D) spin-1/2 models have been constructed to
realize Kitaev’s sixteen-fold way of anyon theories. Defining a one-dimensional
(1D) path through all the lattice sites, and performing the Jordan-Wigner
transformation with the help of the 1D path, we find that such a spin-1/2 model
is equivalent to a model with $\nu$ species of Majorana fermions coupled to a
static $\mathbb{Z}_2$ gauge field. Here each specie of Majorana fermions gives
rise to an energy band that carries a Chern number $\mathcal{C}=1$, yielding a
total Chern number $\mathcal{C}=\nu$. It has been shown that the ground states
are three (four)-fold topologically degenerate on a torus, when $\nu$ is an odd
(even) number. These exactly solvable models can be achieved by quantum
simulations.
