%0 Journal Article
%T Symmetry protection of topological order in one-dimensional quantum spin systems
%A Frank Pollmann
%A Erez Berg
%A Ari M. Turner
%A Masaki Oshikawa
%J Physics
%D 2009
%I arXiv
%R 10.1103/PhysRevB.85.075125
%X 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 non-trivial phase which is protected by any one of the following three global symmetries: (i) the dihedral group of $\pi$-rotations about $x,y$ and $z$ axes; (ii) time-reversal symmetry $S^{x,y,z} \rightarrow - S^{x,y,z}$; (iii) link inversion symmetry (reflection about a bond center), consistently with previous results [Phys. Rev. B \textbf{81}, 064439 (2010)]. On the other hand, an even-$S$ Haldane phase is not topologically protected (i.e., it is indistinct from a trivial, site-factorizable phase). We show some numerical evidence that supports these claims, using concrete examples.
%U http://arxiv.org/abs/0909.4059v3