Special Condensed Matter Seminar: Chang-Tse Hsieh, University of Illinois Urbana-Champaign, “Interacting topological phases and refinements of quantum anomalies”

In this talk, I would present the correspondence between symmetry-protected topological (SPT) phases and their anomalous boundary states, based on examples in various spacetime dimensions. Through the study of the effect of interactions on these SPT phases, we discovered a new formalism of quantum anomalies, associated with discrete spacetime (such as time-reversal and spatial reflection) symmetries in particular, to classify distinct interacting topological phases. For example, the breakdown of the noninteracting classification of (3+1)d time-reversal symmetric topological superconductors by an integer to Z_16, in the presence of interactions, can be characterized by the global gravitational anomalies in the surface theories formulated on unorientable spacetime manifolds – a refinement of the usual “parity” anomaly. I would further discuss anomalies of Weyl fermions with discrete symmetries in 3+1 dimensions, which have not been fully understood so far, and address some possible applications in condensed matter systems.