Signatures of Green's function zeros and their topology using impurity spectroscopy

The notion of topology without quasiparticles, especially in the presence of Green's function zeros, has become central to understanding correlated topology in Mott insulators. Yet, direct experimental detection of these zeros represents a challenge. Using exact diagonalization of the one-dimensional Hubbard model with a nonmagnetic impurity and Zeeman field, complemented by exact analytic results in the atomic limit, we show that a Green's function zero within the Mott gap manifests as additional spectral weight within the Hubbard bands when the impurity potential approaches the on-site Coulomb repulsion (unitary limit). Additionally, the impurity-induced band, along with its associated zero, vanishes above a critical Zeeman field. Our results enable us to propose a concrete pathway to experimentally probe Green's function zeros and their topological character through impurity scattering and magnetic-field tuning.