### Speaker

### Description

While sharply-quantized topological features are conventionally associated with gapped phases of matter, there are a growing number of examples of gapless systems with topologically protected edge states. A particularly striking set of examples are "intrinsically gapless" symmetry-protected topological states (igSPTs), which host topological surface states that could not arise in a gapped system with the same symmetries. Examples include familiar non-interacting Weyl semimetals with Fermi arc surface states, as well as more exotic examples like deconfined quantum critical points with topological edge states. In this talk, I will discuss recent progress in formally understanding the bulk-boundary correspondence of strongly-interacting igSPTs using tools from group cohomology. In these examples, the gapless-ness of the bulk and presence of topological surface states can be understood in a unified way due to the presence of an emergent anomaly. Our formalism allows construction of lattice-models with such emergent anomalies whose topological properties can be deduced exactly.

### External references

- 22110075
- 6d0336ec-089c-4ce5-ae4e-2a7e0e9dd04a
- ca6de301-ae3d-409f-bb9c-1ee773f76b0d