Two-dimensional symmetry-protected topological orders and their protected gapless edge excitations

  title={Two-dimensional symmetry-protected topological orders and their protected gapless edge excitations},
  author={Xie Chen and Zhengxin Liu and Xiao-Gang Wen},
  journal={Physical Review B},
Topological insulators in free fermion systems have been well characterized and classified. However, it is not clear in strongly interacting boson or fermion systems what symmetry-protected topological orders exist. In this paper, we present a model in a two-dimensional (2D) interacting spin system with nontrivial onsite Z{sub 2} symmetry-protected topological order. The order is nontrivial because we can prove that the one-dimensional (1D) system on the boundary must be gapless if the symmetry… 

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this is a reasonable restriction because we want to study systems at fixed point where the correlation length in the bulk is zero

    Note2, the (d + 1)-cohomology group of Z2 H d+1 (G, U (1)) is trivial for odd d and is a Z2 group for even d

      But this is not a problem as we can redefinẽ T (CZX) = iT (CZX) and the extra minus sign

      • Note3, the mapping actually reduces T (CZX, CZX) to −T (I)