Mutual Chern-Simons theory for Z2 topological order

Su Peng Kou, Michael Levin, Xiao Gang Wen

Research output: Contribution to journalArticlepeer-review

66 Scopus citations


We study several different Z2 topological ordered states in frustrated spin systems. The effective theories for those different Z 2 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 different Z2 topological orders are reflected in different projective realizations of lattice symmetry in the same effective mutual Chern-Simons theory. This result is obtained by comparing the ground-state degeneracy, the ground-state quantum numbers, the gapless edge state, and the projective symmetry group of quasiparticles calculated from the slave-particle theory and from the effective mutual Chern-Simons theories. Our study reveals intricate relations between topological order and symmetry.

Original languageEnglish
Article number155134
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number15
StatePublished - 31 Oct 2008
Externally publishedYes


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