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arXiv:2412.12995 · Physical Review X

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

Jinu Thomas, Debshikha Banerjee, Alberto Nocera, Steven Johnston

Published Apr 25, 2025• 7 citations
arXivHTMLPDF

Abstract

An emerging application of resonant inelastic x-ray scattering (RIXS) is the study of lattice excitations and electron-phonon ( e -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 e -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 -ph interactions and set the stage for a more realistic analysis of future experiments.

DOI
10.1103/physrevx.15.021030

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An emerging application of resonant inelastic x-ray scattering (RIXS) is the study of lattice excitations and electron-phonon ( e -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 e -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 -ph interactions and set the stage for a more realistic analysis of future experiments.
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Su-Schrieffer-Heeger-like (SSH-like) electron-phonon interactions can drive the formation of light (bi)polarons and several novel states of matter. It is, therefore, prudent to develop experimental protocols for identifying such couplings in real materials and quantifying their strength. Here, we investigate how resonant inelastic x-ray scattering (RIXS) probes electron-phonon interactions in the one-dimensional half-filled Hubbard-SSH model with on-site phonons. Using the density matrix renormalization group method, we compute the full RIXS response and find that the lattice excitations generated during the scattering process inevitably couple to the system's charge and magnetic sectors, resulting in combined multiparticle excitations that cannot be easily disentangled from one another. While this aspect complicates the interpretation of RIXS experiments, we outline how it can be leveraged to identify and quantify SSH-like interactions in quantum materials.
We use the nonequilibrium dynamical mean-field theory formalism to compute the equilibrium and nonequilibrium resonant inelastic x-ray scattering (RIXS) signal of a strongly interacting fermionic lattice model with a coupling of dispersionless phonons to the total charge on a given site. In the atomic limit, this model produces phonon subbands in the spectral function, but not in the RIXS signal. Electron hopping processes however result in phonon-related modifications of the charge excitation peak. We discuss the equilibrium RIXS spectra and the characteristic features of nonequilibrium states induced by photo-doping and by the application of a static electric field. The latter produces features related to Wannier-Stark states, which are dressed with phonon sidebands. Thanks to the effect of field-induced localization, the phonon features can be clearly resolved even in systems with weak electron-phonon coupling.
Abstract We present a method for computing the resonant inelastic x-ray scattering (RIXS) spectra in one-dimensional systems using the density matrix renormalization group (DMRG) method. By using DMRG to address this problem, we shift the computational bottleneck from the memory requirements associated with exact diagonalization (ED) calculations to the computational time associated with the DMRG algorithm. This approach is then used to obtain RIXS spectra on cluster sizes well beyond state-of-the-art ED techniques. Using this new procedure, we compute the low-energy magnetic excitations observed in Cu L-edge RIXS for the challenging corner shared CuO4 chains, both for large multi-orbital clusters and downfolded t-J chains. We are able to directly compare results obtained from both models defined in clusters with identical momentum resolution. In the strong coupling limit, we find that the downfolded t-J model captures the main features of the magnetic excitations probed by RIXS only after a uniform scaling of the spectra is made.
Abstract Resonant inelastic X-ray scattering (RIXS) detects various types of high- and low-energy elementary excitations in correlated solids, and this tool will play an increasingly important role in investigations of time-dependent phenomena in photo-excited systems. While theoretical frameworks for the computation of equilibrium RIXS spectra are well established, the development of appropriate methods for nonequilibrium simulations is an active research field. Here, we apply a recently developed nonequilibrium dynamical mean field theory (DMFT) based approach to compute the RIXS response of photo-excited two-orbital Mott insulators. The results demonstrate the feasibility of multi-orbital nonequilibrium RIXS calculations and the sensitivity of the quasi-elastic fluorescence-like features and excitation peaks on the nonequilibrium population of the Hubbard bands.
While new light sources allow for unprecedented resolution in experiments with X-rays, a theoretical understanding of the scattering cross-section is lacking. In the particular case of strongly correlated electron systems, numerical techniques are quite limited, since conventional approaches rely on calculating a response function (Kramers-Heisenberg formula) that is obtained from a perturbative analysis of scattering processes in the frequency domain. This requires a knowledge of a full set of eigenstates in order to account for all intermediate processes away from equilibrium, limiting the applicability to small tractable systems. In this work, we present an alternative paradigm, recasting the problem in the time domain and explicitly solving the time-dependent Schrödinger equation without the limitations of perturbation theory: a faithful simulation of the scattering processes taking place in actual experiments, including photons and core electrons. We show how this approach can yield the full time and momentum resolved Resonant Inelastic X-Ray Scattering (RIXS) spectrum of strongly interacting many-body systems. We demonstrate the formalism with an application to Mott insulating Hubbard chains using the time-dependent density matrix renormalization group method, which does not require a priory knowledge of the eigenstates and can solve very large systems with dozens of orbitals. This approach can readily be applied to systems out of equilibrium without modification and generalized to other spectroscopies.