10-10U

We solve for the core-hole propagator and the resonant inelastic X-ray scattering (RIXS) response functions in correlated materials by employing dynamical mean-field theory. We focus our attention on the spinless Falicov-Kimball model, where the problem can be solved exactly, and the system can be tuned to go through a Mott-Hubbard-like metal-insulator transition. The core-hole propagator is expressed in terms of a continuous fermionic Toeplitz determinant defined only on the upper real-time branch of the Keldysh contour which produces an efficient algorithm to obtain the density of states of the X-ray edge problem for any temperature and any interaction strength. We have also derived the two-particle vertices in a diagrammatic representation of the direct and indirect scattering processes. As an example of this formalism, we show results for the direct RI\/XS.