Bipartite Charge Fluctuations and Many-Body Quantum Geometry

In many-body systems with U(1) global symmetry, charge fluctuations in a subregion provide important insights into entanglement and other global properties. In this talk, I will clarify the universal and non-universal features of the shape dependence of charge fluctuations, highlighting an intriguing relationship between bipartite fluctuations and many-body quantum geometry. Although the quantum metric itself is not universal, it adheres to both a universal topological lower bound and an energetic upper bound. I will further discuss the conditions for bound saturation in (anisotropic) Landau levels, leveraging the generalized Kohn theorem and the holomorphic properties of many-body wavefunctions.