Minimalist approach to the classification of symmetry protected topological phases - Charles Zhaoxi Xiong

Topological insulators and superconductors epitomize a large class of phases that fall outside Landau’s symmetry-breaking paradigm. By now it is clear that more than one phases can exist in a phase diagram even without spontaneous symmetry breaking. These are gapped phases at zero temperature distinguished by their topological properties and cannot be tuned to each other without breaking the symmetry or closing the gap. The topological properties manifest themselves in such forms as gapless boundary modes or anyonic excitations, which have garnered considerable interest due to their potential application to quantum computation.
In this talk, we will consider an interacting generalization of topological insulators and superconductors called “symmetry protected topological” (SPT) phases, which have been under intense investigation in recent years. I will first review efforts in the field to classify SPT phases, and then indicate how a seemingly abstract object in mathematics can unify various existing classification proposals and shed new light on the classification problem.
References: 1701.00004 (theoretical framework), 1709.06998 (application to hourglass fermions KHgSb)