Topological Bound on the Structure Factor

We show that the static structure factor of general many-body systems with U(1) symmetry has a lower bound determined only by the ground state Chern number. Our bound relies only on causality and non-negative energy dissipation, and holds for a wide range of two-dimensional gapped systems. We apply our theory to (fractional) Chern insulators, (fractional) quantum spin Hall insulators, topological superconductors, and chiral spin liquids. Our results uncover a universal feature of topological phases beyond the quantized response.