Time-dependent scattering approach to compute RIXS spectra

Reliable methods to calculate Resonant Inelastic X-Ray Scattering (RIXS) spectra in strongly correlated many-body systems have been constrained to relatively small problems, as they rely on evaluating a response function (Kramers-Heisenberg formula) that is obtained from a time-dependent perturbative analysis of the scattering problem. This requires the knowledge of all eigenstates of the many-body Hamiltonian to account for intermediate processes involving excitations of core electrons. We introduce a novel approach recasting such calculation as an effective time-dependent problem in which incoming photons scatter with the system and outgoing photons are captured by a detector. The spectral density is obtained by solving the time-dependent Schroedinger equation explicitly involving the photon degree of freedom. We demonstrate the formalism with an application to Mott insulating Hubbard chains using the time-dependent density matrix renormalization group method. Our approach can readily be applied to systems out of equilibrium without modification and generalized to other spectroscopies.