An anyon model in a toric honeycomb lattice

We study an anyon model in a toric honeycomb lattice. The ground states and the low-lying excitations coincide with those of Kitaev toric code model and then the excitations obey mutual semionic statistics. This model is helpful to understand the toric code of anyons in a more symmetric way. On the other hand, there is a direct relation between this toric honeycomb model and a boundary coupled Ising chain array in a square lattice via Jordan-Wigner transformation. We discuss the equivalence between these two models in the low-lying sector and realize these anyon excitations in a conventional fermion system.