Entanglement Witness and Multi-point Correlations in Resonant Inelastic X-Ray Scattering

Characterizing entanglement in quantum materials is crucial for next-generation quantum technologies. However, defining and measuring a quantifiable figure of merit for entanglement in a many-body quantum system is theoretically and experimentally challenging. The presence of entanglement in fermionic systems can be diagnosed by extracting entanglement witnesses from spectroscopies, which are directly related to the spin dynamic structure factors of the system. With cross-polarization, RIXS(Resonant inelastic X-ray scattering) approximates the spin and charge dynamic structure factors, which becomes exact at the ultra-short core-hole lifetime limit. Here, we propose a new RIXS technique that can extract higher-order correlations beyond the scope of the spin and charge structure factors. We verify our method using computational RIXS spectra, and theoretically propose a new entanglement witness of fermion systems. Using the extended Hubbard model and Kitaev honeycomb model as examples, we show the entanglement witness can quantify the multipartite entanglement in different phase regions.