Entanglement Witness for Indistinguishable Electrons using Solid-State Spectroscopy (2)

Characterizing entanglement in quantum materials is crucial for advancing next-generation quantum technologies. Despite recent strides in witnessing entanglement in magnetic materials with distinguishable spin modes, quantifying entanglement in systems formed by indistinguishable electrons remains a formidable challenge. In Part 1, we introduce a method to extract cumulant two-particle reduced density matrix (RDM) from resonant inelastic X-ray scattering (RIXS) spectra. In Part 2, we focus on the theoretical bounds in these eigenvalues of CRDM and demonstrate the linear scaling with fermionic entanglement depth, providing a reliable witness for entanglement. In addition, we discuss multipartite entanglement in systems of indistinguishable particles, and using the material-relevant strongly correlated models as examples, we show how this entanglement witness can efficiently quantify multipartite entanglement across different phase regions, highlighting its advantage over quantum Fisher information (QFI).