Title:Oral: Low-Energy Electromagnetic Response in Moiré Materials

We investigate the low-energy electromagnetic response in moiré materials, focusing on the partial sum rule associated with the inverse frequency-weighted optical conductivity at low energies. We present results for this sum rule in a non-perturbative yet “solvable” limit across various correlation-induced insulators. Our findings reveal that for a certain class of insulators, the partial sum rule is governed by a “many-body projected quantum geometry” derived from the interaction-renormalized electronic bands. We also extend these results to include contributions from coupling to high-energy degrees of freedom using a renormalization group inspired method.