Mutual Chern-Simons theory for Z2 topological order and doped Mott insulator

Abstract: The Chern-Simons theory has been sucessful to describe the quantum fractional hall effect. Here another kind of topological field theory - mutual Chern-Simons theory would be talked about. The mutual Chern-Simons theory has U(1)*U(1) gauge structure with T and P symmetry, of which the mutual semion statistics is the key point. The doped Mott insulator is an example for the mutual Chern-Simons theory in Higgs phase. It is shown that from a bosonic slave technique, holon and spinon have mutual Chern-Simons statistics. A global phase diagram for the doped Mott insulator is obtained. Z2 topological order is an example for the mutual Chern-Simons theory in gapped phase. It is shown that the mutual Chern-Simons theory has the same topological properties as those for Z2 topological order, such as the topological degeneracy, mutual semion statistics and the edge states.