Berlin 2012 – wissenschaftliches Programm

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HL: Fachverband Halbleiterphysik

HL 53: Transport: Topological Insulators 3 (jointly with TT, MA)

HL 53.8: Vortrag

Mittwoch, 28. März 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.