  We propose a protocol for detecting multipartite entanglement in itinerant
many-body electronic systems using the quantum Fisher information (QFI). We
establish a connection between the QFI and single-particle Green's functions by
identifying a set of non-trivial witness operators. To construct these
operators, we employ a doubling of the system wherein we introduce two
identical copies of the original model. While the witness operator hops
electrons between copies, the copies do not interact with one another. We apply
this methodology to a finite-sized fermionic system and showcase its
effectiveness in detecting entanglement in spinless itinerant electron models.
We show that the detected entanglement level is sensitive to the wave vector
associated with the hopping process. We also demonstrate the important role
that symmetry has in detecting levels of entanglement. Our protocol paves the
way for detecting entanglement in many-body systems using scanning tunneling
microscopy and angle-resolved photoemission spectroscopy, thus offering
exciting prospects beyond the detection of entanglement via the dynamical spin
response accessed in neutron scattering experiments.
