Quantum anomalies in interacting topological semimetals

In this talk we explore the following question: can strong electron-electron interactions open a gap in topological semimetals while mantaining their topological response without breaking the protecting symmetries, or introducing topological order? We demonstrate that the answer is no, and show that what prevents it is the topological response, arising from quantum anomalies. While this is familiar in the case of magnetic Weyl semimetals, where the topological response takes the form of an anomalous Hall effect, analogous responses in other types of topological semimetals are more subtle and involve crystal symmetry as well as electromagnetic gauge fields. Physically these responses may be related to magnetoelastic properties of topological semimetals, and are detectable in the presence of appropriate symmetry defect loop linkings. We provide a comprehensive summary of symmorphic symmetry-protected semimetal topological responses which fully determine the topological order of realisable strongly-correlated gapped states.