Intrinsically gapless symmetry-protected topology

          @misc{ pirsa_PIRSA:22110075,
            doi = {10.48660/22110075},
            url = {https://pirsa.org/22110075},
            author = {Potter, Andrew},
            keywords = {Condensed Matter},
            language = {en},
            title = {Intrinsically gapless symmetry-protected topology},
            publisher = {Perimeter Institute},
            year = {2022},
            month = {nov},
            note = {PIRSA:22110075 see, \url{https://pirsa.org}}
          }
          

Abstract

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.