2009/09/30 by Frank Pollmann, Erez Berg, Ari M. Turner +1 · 2 citations
Physics and Astronomy · #cond-mat.str-el #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.85.075125
published as Phys. Rev. B 85, 075125 (2012) · 9 pages, 6 figures, extended version: several new examples and numerical results added. Journal reference added
arxiv created 2012/03/21 · arxiv updated 2012/03/22
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 π-rotations about x,y and z axes; (ii) time-reversal symmetry Sx,y,z → - Sx,y,z; (iii) link inversion symmetry (reflection about a bond center), consistently with previous results [Phys. Rev. B 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.