Projected p-wave superconducting wave-functions for topological orders

In this paper we develop a sysmatical theory for topological orders by the projected p-wave superconducting (SC) wave-functions and unify the different topological orders for spin models into the fermionic picture. We found that the energy for the fermions at k=(0,0), (0, pi), (pi, 0), (pi, pi) acts as a topological invariable to characterize 16 universal classes of different topological orders for the spin models with translation invariance. Based on the projected p-wave SC wave-functions the topological properties for the known topological orders in the exact solved spin models are obtained. Finally new types of topological orders are predicted.