Geometric curvature driven by many-body collective fluctuations

Quantum geometry characterizes the variation of wavefunctions in momentum space through their overlaps and relative phases, providing a general framework for understanding many transport and optical properties. It is generally formulated in terms of interband matrix elements, which, entering the response functions, allow obtaining experimental access to the quantum geometric tensor. Recently, it has been emphasized that quantum geometry can also be interpreted in terms of quantum dipole fluctuations in the ground state driven by interband mixing. Here, we extend this picture to include contributions from many-body collective fluctuations, in which propagators and response vertices are dressed dynamically by the interaction with collective modes. Focusing on the Berry curvature, we show that contributions from collective fluctuations can be experimentally distinguished from bare band-geometric contributions, via specific antisymmetric channels in inelastic scattering spectra. We further identify the non-commutative properties of transverse quantum fluctuations as well as non-local-time interactions as the generators of this dynamical curvature in the susceptibility response.