Talk Title: Topological phases: An entanglement point of view We propose a scheme to classify gapped phases of one dimensional
systems in terms of properties of the entanglement spectrum. We discuss the
application of this scheme to the classification of phases in two specific examples.
The first example is the Haldane phase of S=1 chains. 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. |