Theory of Electron-Phonon Interactions in Extended Correlated Systems Probed by Resonant Inelastic X-Ray Scattering

An emerging application of resonant inelastic x-ray scattering (RIXS) is the study of lattice excitations and electron-phonon (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>e</a:mi></a:math>-ph) interactions in quantum materials. Despite the growing importance of this area of research, the community lacks a complete understanding of how the RIXS process excites the lattice and how these excitations encode information about the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>e</c:mi></c:math>-ph interactions. Here, we present a detailed study of the RIXS spectra of the Hubbard-Holstein model defined on extended one-dimensional lattices. Using the density matrix renormalization group method, we compute the RIXS response while treating the electron mobility, many-body interactions, and core-hole interactions on an equal footing. The predicted spectra exhibit notable differences from those obtained using the commonly adopted Lang-Firsov models, with important implications for analyzing past and future experiments. Our results provide a deeper understanding of how RIXS probes <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>e</e:mi></e:math>-ph interactions and set the stage for a more realistic analysis of future experiments.