Electron-phonon excitations in the 1D Hubbard-Holstein model probed by Resonant Inelastic X-Ray Scattering

The prospect of accessing electron-phonon (e-p) coupling strengths using resonant inelastic x-ray scattering (RIXS) has attracted significant attention in recent years. With current energy resolution, RIXS experiments can now resolve individual phonon modes. Standard analysis for such experiments is done by using a single site Lang Firsov (LF) model that promises to extract quantative information on momentum resolved e-p coupling by fitting data. This method, however, computes the phonon RIXS intensities by approximating the electron-phonon interaction in the atomic limit, coupling a single electronic excitation to a single phonon mode. It remains unclear if such a drastic approximation remains valid for a many-particle system with itinerant carriers. We test the validity of this model in the strongly correlated many-particle limit. By explicitly computing the RIXS intensity using DMRG, we study the phonon excitations in finite-sized Hubbard-Holstein chains and compare our results against the single-site and the single-band predictions.