Adventures in Gapless Topological Phases

A fascinating feature of some gapped systems is topological order, where the system flows to a nontrivial TQFT in the infrared. The gap is often essential to the description of these phases, so it is interesting to ask what happens to them when the gap closes, and if there are more general topological phases which require the absence of a gap. In this talk, I will describe recent progress in exploring such phases. The talk will follow two main themes: the fate of a gapped SPT phase at a symmetry breaking transition, and intrinsically gapless SPT phases in the presence of an emergent anomaly. I will describe a conjectural bulk-boundary correspondence which explains the edge modes in both of these cases.

This talk is based on arXiv:2008.06638 and arXiv:1905.06969.