Dresden 2011 – scientific programme
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TT: Fachverband Tiefe Temperaturen
TT 55: TR: Topological Insulators 1 (jointly with HL and MA)
TT 55.2: Talk
Thursday, March 17, 2011, 16:15–16:30, HSZ 304
Symmetry protected topological phases: An entanglement point of view — •Frank Pollmann1, Ari Turner2, Erez Berg3, and Masaki Oshikawa4 — 1Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany — 2Department of Physics, University of California, Berkeley CA 94720, USA — 3Department of Physics, Harvard University, Cambridge, MA 02138, USA — 4Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581 Japan
We propose a scheme to characterize topological phases in one dimensional systems in terms of properties of the entanglement spectrum. We discuss the application of this scheme in two specific examples. The first example is the Haldane phase for a S=1 chain. We show that the Haldane phase is protected by certain symmetries and characterized by a double degeneracy of the entanglement spectrum. The degeneracy cannot be lifted unless either a phase boundary to another, "topologically trivial", phase is crossed or the symmetry is broken. In the second example we apply these concepts to classify systems of interacting fermions in one dimension in the presence of time reversal and parity symmetry.