High-order strong-coupling expansion for x-ray absorption on a dynamically screened impurity

Time-resolved x-ray absorption can reveal the dynamical screening of the local Coulomb interaction in strongly correlated photodoped materials. Here, we focus on the theoretical prediction of x-ray absorption in the presence of dynamical screening using the strong-coupling expansion, i.e., an expansion around the isolated absorption site in terms of the retarded interaction. The evaluation of higher-order diagrams is made numerically feasible by an approach based on the decomposition of the retarded interaction into complex exponentials. With this, we evaluate the strong-coupling series to third order on an electron-boson model of Holstein type. We demonstrate that in relevant coupling regimes, even low orders of the strong-coupling expansion can give a significant correction over the previously used lowest-order approximation.