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arXiv:2012.10067 · Europhysics Letters (EPL)

Nonequilibrium-DMFT based RIXS investigation of the two-orbital Hubbard model

Philipp Werner, Steven Johnston, Martin Eckstein

Published Mar 1, 2021• 12 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1209/0295-5075/133/57005

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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.
We develop a framework to evaluate the time-dependent resonant inelastic x-ray scattering (RIXS) signal with the use of nonequilibrium dynamical mean-field theory simulations. The approach is based on the solution of a time-dependent impurity model which explicitly incorporates the probe pulse. It avoids the need to compute four-point correlation functions and can in principle be combined with different impurity solvers. This opens a path to study time-resolved RIXS processes in multiorbital systems. The approach is exemplified with a study of the RIXS signal of a melting Mott antiferromagnet.
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.
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.
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.
We present a formalism based on nonequilibrium dynamical mean-field theory (DMFT) which allows to compute the time-resolved x-ray absorption spectrum (XAS) of photoexcited solids. By applying this formalism to the photodoped half-filled and quarter-filled two-orbital Hubbard models in the Mott insulating regime we clarify how the time-resolved XAS signal reflects the nonequilibrium population of different local states. Apart from the missing broadening associated with continuum excitations, the atomic XAS spectrum computed with the nonthermal state populations provides a good approximation to the full nonequilibrium DMFT result. This suggests a route to combine the accurate DMFT description of nonequilibrium states of solids with cluster calculations of the XAS signal.
Quasi-one-dimensional systems exhibit many-body effects elusive in higher dimensions. A prime example is spin-orbital separation, which has been measured by resonant inelastic x-ray scattering (RIXS) in Sr2CuO3{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}Sr2​CuO3​. Here, we theoretically analyze the time-resolved RIXS spectrum of Sr2CuO3{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}Sr2​CuO3​ under the action of a time-dependent electric field. We show that the external field can reversibly modify the parameters in the effective $t\text{\ensuremath{-}}J$ model used to describe spinon and orbiton dynamics in the material. For strong driving amplitudes, we find that the spectrum changes qualitatively as a result of reversing the relative spinon to orbiton velocity. The analysis shows that in general, the spin-orbital dynamics in Mott insulators in combination with time-resolved RIXS should provide a suitable platform to explore the reversible control of many-body physics in the solid with strong laser fields.