Berlin 2012 – scientific programme
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TT: Fachverband Tiefe Temperaturen
TT 26: Transport: Topological Insulators 3 (jointly with HL and MA)
TT 26.8: Talk
Wednesday, March 28, 2012, 11:30–11:45, BH 334
Generalized string order in 1D symmetry protected topological phases — •Frank Pollmann1, Ari Turner2, and Erez Berg3 — 1Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany — 2University of Amsterdam, 1090 GL Amsterdam, The Netherlands — 3Department of Physics, Harvard University, Cambridge, MA 02138, USA
A topological phase is a phase of matter which cannot be characterized by a local order parameter. It has been shown that gapped phases in 1D systems can be completely characterized using tools related to projective representations of the symmetry groups. An example of a symmetry protected topological phase is the Haldane phase of S = 1 chains. Here the phase is protected by any of the following symmetries: dihedral group of π-rotations about two orthogonal axes, time-reversal symmetry, or bond centered inversion symmetry. We introduce non-local order parameters as generalization of string order for each case which can be simply calculated using numerical methods such as Density-Matrix Renormalization Group (DMRG). These non-local order parameters provide a practical tool for numerically detecting different phases.