Symmetry protection of topological phases in one-dimensional quantum spin systems

  title={Symmetry protection of topological phases in one-dimensional quantum spin systems},
  author={F. Pollmann and Erez Berg and Ari M. Turner and Masaki Oshikawa},
  journal={Physical Review B},
We discuss the characterization and stability of the Haldane phase in integer spin chains on the basis of simple, physical arguments. We find that an odd-S Haldane phase is a topologically nontrivial phase which is protected by any one of the following three global symmetries: (i) the dihedral group of π rotations about the x, y, and z axes, (ii) time-reversal symmetry Sx,y,z→−Sx,y,z, and (iii) link inversion symmetry (reflection about a bond center), consistent with previous results [ Phys… 

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