Quantum entanglement and quantum geometry measured with inelastic X-ray scattering

Using previously collected inelastic X-ray scattering (IXS) spectra, we investigated the quantum geometry and quantum information in the large-gap insulator, LiF. In this talk, I will describe how using sum rules for the density-density response function measured in IXS, we computed the quantum Fisher information of the equilibrium density matrix of LiF associated with density perturbations. Further, I will describe how, by exploiting universal relations between the quantum Fisher information, the optical conductivity, and the quantum metric tensor, we extrapolated the diagonal (h,k,l) = (1,0,0) component of the quantum metric of LiF, known as the quantum weight. I will show a comparison between results and recently proposed bounds on the quantum weight, which shows that LiF resides near the lower bound, supporting the general understanding of this material as a highly localized, ionic insulator. Our work serves as a proof-of-principle that IXS techniques can be used to quantify state-of-the-art quantum geometric quantities of materials.