Macroscopic Quantum Tunneling Effect of Z2 Topological Order

In this paper, macroscopic quantum tunneling (MQT) effect of Z2 topological order in the Wen-Plaquette model is studied. This kind of MQT is characterized by quantum tunneling processes of different virtual quasi-particles moving around a torus. By a high-order degenerate perturbation approach, the effective pseudo-spin models of the degenerate ground states are obtained. From these models, we get the energy splitting of the ground states, of which the results are consistent with those from exact diagonalization methodComment: 25 pages, 14 figures, 4 table