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

✍ Scribed by Pollmann, Frank; Berg, Erez; Turner, Ari M.; Oshikawa, Masaki

• Book ID: 127119418
• Publisher: The American Physical Society
• Year: 2012
• Tongue: English
• Weight: 605 KB
• Volume: 85
• Category: Article
• ISSN: 1098-0121
• DOI: 10.1103/physrevb.85.075125

✦ Synopsis

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 S x,y,z → −S x,y,z , and (iii) link inversion symmetry (reflection about a bond center), consistent 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.