Using X-Ray Spectroscopies to Quantify Quantum Fisher Information

Understanding and controlling entanglement in quantum materials is crucial for advancing quantum technologies. To quantify entanglement in many-body materials, we calculated Quantum Fisher Information (QFI) in order to witness entanglement. Using Density Matrix Renormalization Group (DMRG), we systematically investigate the dynamical spin structure factor in the extended Hubbard model, motivated by the significant near-neighbor attractive Coulomb interaction V observed in recent cuprate photoemission experiments. To validate our theoretical model, we compute QFI from the obtained via DMRG and compare it with QFI results derived from Resonant Inelastic X-ray Scattering (RIXS) experiments. Considering the Cu L-edge RIXS is a mixture of spin-flip and spin-conserved channels, we apply a q dependent normalization factor to the RIXS results. The QFI from normalized RIXS matches the DMRG-simulated QFI thus confirming the reliability of our approach.