Exciton cumulant for many-body effects in K- and L-edge X-ray absorption spectroscopy

Many-body satellite peaks are prevalent in x-ray spectroscopy and are especially important in x-ray photoelectron spectroscopy. These satellite features, which come from excitations beyond any effective single-particle theory are also sometimes prominent in x-ray absorption spectroscopy (XAS), especially that of highly correlated materials such as transition metal oxides. The cumulant expansion for the one-electron Green's function has shown great promise in treating these satellite peaks in both XPS and XAS, predicting multiple plasmon excitations in the XPS of free-electron like materials, as well as charge-transfer excitations in more strongly correlated materials. However, the theory for treating these satellites in XAS is complicated by the fact that both the core-hole and photoelectron interact with the valence electrons to create these many-body excitations, and the interference between these modes of excitation is strong. Here we present a cumulant expansion of the exciton Green's function for deep-core spectroscopy, based on a Bethe-Salpeter calculation of the exciton density, and a real-time TDDFT calculation of the cumulant. Finally, the many-body absorption spectrum is given as a convolution of the cumulant spectral function with the quasiparticle absorption spectrum. We show that in the very near edge, the bound excitons strongly screen the core-hole, suppressing the many-body excitations, while farther from the edge, the interference is lessened. We also show comparison between various theories as well as to experiment for a variety of materials.