Dr. Frank Pollmann (Max Planck Institute for the Physics of Complex Systems, Germany)
"Topological Phases of One-Dimensional Fermions: An Entanglement Point of View"

The effect of interactions on topological insulators and superconductors remains, to a large extent, an open problem. Here, we describe a framework for classifying phases of one-dimensional interacting fermions, focusing on spinless fermions with time-reversal symmetry and particle number parity conservation, using concepts of entanglement. We find that in the presence of interactions there are only eight distinct phases, which obey a Z8 group structure. This is in contrast to the Z classification in the non-interacting case. Each of these eight phases is characterized by a unique set of bulk invariants, related to the transformation laws of its entanglement (Schmidt) eigenstates under symmetry operations. In addition we discuss some preliminary results obtained for an effective "parafermionic" model at the boundary of a fractional-topological insulator.