Abstract:
Charge fluctuations, namely, the variance of particle number within a chosen spatial region, provide a fundamental probe of quantum many-body systems. They capture correlations across the boundary of a subsystem and offer an experimentally accessible alternative to entanglement-based diagnostics. In this talk, I will show that, in three-dimensional non-interacting multi-band metals, detailed information about the shape and quantum geometry of Fermi surfaces is encoded in the subleading logarithmic term of these bipartite charge fluctuations. This logarithmic contribution is directly related to the dimensionless coefficient of the |q|^3 term in the structure factor in momentum space. Remarkably, both quantities admit a unified description in terms of Fermi-surface integrals involving the curvature tensor and the quantum metric tensor. In this way, charge fluctuations provide a window into the underlying quantum geometry of electronic states. I will also discuss how charge fluctuations reveal universal properties of quantum critical points described by conformal field theories with a conserved U(1) charge.