Author(s): Yi-Chun Hung, Yugo Onishi, Hsin Lin, Liang Fu, and Arun Bansil The quantum metric encodes the geometric structure of Bloch wave functions and governs a wide range of physical responses. Its Brillouin-zone integral, the quantum weight, appears in the structure factor and provides lower bounds on observables such as the optical gap and dielectric constant. In sym… [Phys. Rev. Lett. 137, 126601] Published Mon Sep 14, 2026