Mutual Chern-Simons theory for Z2 topological order
We study several di erent Z2 topological ordered states in frustrated spin systems. The e ective theories for those di erent Z2 topological orders all have the same form-a Z2 gauge theory which can also be written as a mutual U(1)×U(1) Chern-Simons theory. However, we find that the di erent Z2 topological orders are reflected in di erent projective realizations of lattice symmetry in the same e ective mutual Chern-Simons theory. This result is obtained by comparing the groundstate degeneracy, the ground-state quantum numbers, the gapless edge state, and the projective symmetry group of quasi-particles calculated from the slave-particle theory and from the e ective mutual Chern-Simons theories. Our study reveals intricate relations between topological order and symmetry.
版权说明：以下全部内容由寇谡鹏上传于 2010年01月04日 14时26分40秒，版权归本人所有。