Multipartite Entanglement Spectroscopy with Single Particle Green's Functions

We demonstrate how to use the single particle electronic response functions to determine an itinerant electronic system's multipartite entanglement. We do so by computing the quantum Fisher information of a witness operator associated with the single particle Green's function. To allow the QFI to be an effective probe of the multipartite entanglement, we compute it for a doubled system, where there are two copies of the original model and the QFI witness operator hops electrons between the copies which otherwise do not interact. We apply this methodology to finite sized fermionic systems to demonstrate its ability to detect entanglement. We show that the amount of entanglement detected is sensitive to the wave vector of the hopping. This opens the possibility of using scanning tunneling microscopy and angle resolved photoemission probes to detect entanglement in many-body systems.