Detecting Multipartite Entanglement Patterns using Single Particle Green's Functions

We present a protocol for detecting multipartite entanglement in itinerant many-body electronic systems using single particle Green's functions. To achieve this, we first establish a connection between the quantum Fisher information (QFI) and single particle Green's functions by constructing a set of witness operators built out of single electron creation and destruction operators in a doubled system. This set of witness operators is indexed by a momenta $k$. We compute the QFI for these witness operators and show that for thermal ensembles it can be expressed as an auto-convolution of the single particle spectral function. We then apply our framework to a one-dimensional fermionic system to showcase its effectiveness in detecting entanglement in itinerant electron models. We observe that the detected entanglement level is sensitive to the wave vector associated with witness operator. Our protocol will permit detecting entanglement in many-body systems using scanning tunneling microscopy and angle-resolved photoemission spectroscopy, two spectroscopies that measure the single particle Green's function. It offers the prospect of the experimental detection of entanglement through spectroscopies beyond the established route of measuring the dynamical spin response.