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 excitationscoincide with those of Kitaev toric code model and then the excitations obey mutual semionic statistics.This model ishelpful to understand the toric code of anyons in a more symmetric way.On the other hand,there is a direct relationbetween this toric honeycomb model and a boundary coupled Ising chain array in a square lattice via Jordan-Wignertransformation.We discuss the equivalence between these two models in the low-lying sector and realize these anyonexcitations in a conventional fermion system.The analysis for the ground state degeneracy in the last section can alsobe thought of as a complementarity of our previous work [Phys.A: Math.Theor.43(2010)105306].