Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B./Physical review. B

Functional derivative approach to Raman response in nonequilibrium many-body systems described by dynamical mean-field theory

O. P. Matveev, Andrij M. Shvaika, James K. Freericks

Published Apr 30, 2026• 0 citations
Publisher

Abstract

We employ functional derivatives to calculate spectroscopy in nonequilibrium many-body systems. This allows for all vertex correction effects to be properly incorporated. We focus on electronic Raman scattering. As a concrete example, we present numerical results for the nonresonant contribution to the time-resolved electronic Raman scattering cross section in the A 1 g symmetry channel solved with dynamical mean-field theory. To do this, we add a small field to the Hamiltonian and take the functional derivative of the “Raman current” operator with respect to this field, which results in an exact expression for the greater Green's function that determines the Raman scattering cross section. This approach avoids the need to set up and solve Bethe-Salpeter equations, which are notoriously difficult to work with in nonequilibrium. We also work out formal expressions for the optical conductivity in the Appendix.

DOI
10.1103/n17w-5qhk

Related papers

Nonresonant pump/probe electronic Raman scattering within nonequilibrium dynamical mean-field theory

James K. Freericks, O. P. Matveev, Andrij M. Shvaika +1 more

We develop the theory for nonresonant Raman scattering of strongly correlated electrons in time-resolved pump- probe experiments. The electrons are initially pumped with an intense pulse of light and then a probe pulse measures the Raman response function after an adjustable time delay. We describe how the width of the probe pulse and the strength of the electron correlations affect the Raman cross section. The theory is developed for the case of B1g symmetry, where incident and scattered light are polarized perpendicular to each other. We illustrate the exact solution with the Falicov-Kimball model, which is solved via nonequilibrium dynamical mean-field theory.

Ultrafast Bandgap Photonics•May 8, 2018•3 citations

Electronic Raman scattering in correlated materials: A treatment of nonresonant, mixed, and resonant scattering using dynamical mean-field theory

Andrij M. Shvaika, O. Vorobyov, James K. Freericks +1 more

We solve for the electronic Raman scattering response functions on an infinite-dimensional hypercubic lattice employing dynamical mean-field theory. This contribution extends previous work on the nonresonant response to include the mixed and resonant contributions. We focus our attention on the infinite-dimensional spinless Falicov-Kimball model, where the problem can be solved exactly, and the system can be tuned to go through a Mott-Hubbard-like metal-insulator transition. Resonant effects vary in different scattering geometries, corresponding to the symmetries of the charge excitations scattered by the light. We do find that the Raman response is large near the double resonance, where the transfered frequency is close to the incident photon frequency. We also find a joint resonance of both the charge-transfer peak and the low-energy peak when the incident photon frequency is on the order of the interaction strength. In general, the resonance effects can create order of magnitude (or more) enhancements of features in the nonresonant response, especially when the incident photon frequency is somewhat larger than the frequency of the nonresonant feature. Finally, we find that the resonant effects also exhibit isosbestic behavior, even in the ${A}_{1\mathrm{g}}$ and ${B}_{2\mathrm{g}}$ sectors, and it is most prominent when the incident photon frequency is on the order of the interaction energy.

arXiv:cond-mat/0408400•Physical Review B•Jan 25, 2005•32 citations

Nonequilibrium DMFT approach to time-resolved Raman spectroscopy

Philipp Werner, Martin Eckstein, Naoto Tsuji

Raman spectroscopy uses light scattering to extract information on low-energy excitations of solids. The Raman process is described by diagrams which are fourth order in the light-matter interaction and in particular the resonant contribution, which involves four different space-time arguments, is difficult to evaluate. If one instead simulates explicitly the incoming (classical) light pulse, the Raman signal is given by the outgoing photon flux and can be determined from a two-point correlation function. Such a formalism can be used to compute the time-resolved Raman spectrum of nonequilibrium systems, as well as nonlinear signals which are higher order in the incoming field, such as hyper-Raman scattering. Here we explain how to implement this time-dependent formalism within the dynamical mean field theory framework. The method is illustrated with applications to the Holstein-Hubbard model in the strong electron-phonon coupling regime. We demonstrate hyper-Raman scattering in measurements with strong probe fields and frequency mixing signals in the presence of a pump field and simulate the evolution of Stokes and anti-Stokes features after photoexcitations of metallic and Mott insulating systems.

arXiv:2309.02866•Physical review. B./Physical review. B•Dec 27, 2023•2 citations

Theory of time-resolved optical spectroscopy on correlated electron systems

Martin Eckstein, Marcus Kollar

The real-time dynamics of interacting electrons out of equilibrium contains detailed microscopic information about electronically correlated materials, which can be read out with time-resolved optical spectroscopy. The reflectivity that is typically measured in pump-probe experiments is related to the nonequilibrium optical conductivity. We show how to express this quantity in terms of real-time Green's functions using dynamical mean-field theory. As an application we study the electrical response of the Falicov-Kimball model during the ultrafast buildup of the gapped phase at large interaction.

arXiv:0808.1005•Physical Review B•Nov 25, 2008•72 citations

Theory of time-resolved Raman scattering in correlated systems: Ultrafast engineering of spin dynamics and detection of thermalization

Yao Wang, Thomas Devereaux, Cheng-Chien Chen

Ultrafast characterization and control of many-body interactions and elementary excitations are critical to understanding and manipulating emergent phenomena in strongly correlated systems. In particular, spin interaction plays an important role in unconventional superconductivity, but efficient tools for probing spin dynamics, especially out of equilibrium, are still lacking. To address this question, we develop a theory for nonresonant time-resolved Raman scattering, which can be a generic and powerful tool for nonequilibrium studies. We also use exact diagonalization to simulate the pump-probe dynamics of correlated electrons in the square-lattice single-band Hubbard model. Different ultrafast processes are shown to exist in the time-resolved Raman spectra and dominate under different pump conditions. For high-frequency and off-resonance pumps, we show that the Floquet theory works well in capturing the softening of bimagnon excitation. By comparing the Stokes and anti-Stokes spectra, we also show that effective heating dominates at small pump fluences, while a coherent many-body effect starts to take over at larger pump amplitudes and frequencies on resonance to the Mott gap. Time-resolved Raman scattering thereby provides the platform to explore different ultrafast processes and design material properties out of equilibrium.

arXiv:1808.02604•Physical review. B./Physical review. B•Dec 4, 2018•14 citations

Nonequilibrium dynamical mean-field theory of a strongly correlated system

Petra Schmidt, H. Monien

We present a generalized dynamical mean-field approach for the nonequilibrium physics of a strongly correlated system in the presence of a time-dependent external field. The Keldysh Green's function formalism is used to study the nonequilibrium problem. We derive a closed set of self-consistency equations in the case of a driving field with frequency Omega and wave vector q. We present numerical results for the local frequency-dependent Green's function and the self-energy for different values of the field amplitude in the case of a uniform external field using the iterated perturbation theory. In addition, an expression for the frequency-dependent optical conductivity of the Hubbard model with a driving external field is derived.

arXiv:cond-mat/0202046•Feb 4, 2002•23 citations
We employ functional derivatives to calculate spectroscopy in nonequilibrium many-body systems. This allows for all vertex correction effects to be properly incorporated. We focus on electronic Raman scattering. As a concrete example, we present numerical results for the nonresonant contribution to the time-resolved electronic Raman scattering cross section in the A 1 g symmetry channel solved with dynamical mean-field theory. To do this, we add a small field to the Hamiltonian and take the functional derivative of the “Raman current” operator with respect to this field, which results in an exact expression for the greater Green's function that determines the Raman scattering cross section. This approach avoids the need to set up and solve Bethe-Salpeter equations, which are notoriously difficult to work with in nonequilibrium. We also work out formal expressions for the optical conductivity in the Appendix.
We develop the theory for nonresonant Raman scattering of strongly correlated electrons in time-resolved pump- probe experiments. The electrons are initially pumped with an intense pulse of light and then a probe pulse measures the Raman response function after an adjustable time delay. We describe how the width of the probe pulse and the strength of the electron correlations affect the Raman cross section. The theory is developed for the case of B1g symmetry, where incident and scattered light are polarized perpendicular to each other. We illustrate the exact solution with the Falicov-Kimball model, which is solved via nonequilibrium dynamical mean-field theory.
We solve for the electronic Raman scattering response functions on an infinite-dimensional hypercubic lattice employing dynamical mean-field theory. This contribution extends previous work on the nonresonant response to include the mixed and resonant contributions. We focus our attention on the infinite-dimensional spinless Falicov-Kimball model, where the problem can be solved exactly, and the system can be tuned to go through a Mott-Hubbard-like metal-insulator transition. Resonant effects vary in different scattering geometries, corresponding to the symmetries of the charge excitations scattered by the light. We do find that the Raman response is large near the double resonance, where the transfered frequency is close to the incident photon frequency. We also find a joint resonance of both the charge-transfer peak and the low-energy peak when the incident photon frequency is on the order of the interaction strength. In general, the resonance effects can create order of magnitude (or more) enhancements of features in the nonresonant response, especially when the incident photon frequency is somewhat larger than the frequency of the nonresonant feature. Finally, we find that the resonant effects also exhibit isosbestic behavior, even in the A1g{A}_{1\mathrm{g}}A1g​ and B2g{B}_{2\mathrm{g}}B2g​ sectors, and it is most prominent when the incident photon frequency is on the order of the interaction energy.
Raman spectroscopy uses light scattering to extract information on low-energy excitations of solids. The Raman process is described by diagrams which are fourth order in the light-matter interaction and in particular the resonant contribution, which involves four different space-time arguments, is difficult to evaluate. If one instead simulates explicitly the incoming (classical) light pulse, the Raman signal is given by the outgoing photon flux and can be determined from a two-point correlation function. Such a formalism can be used to compute the time-resolved Raman spectrum of nonequilibrium systems, as well as nonlinear signals which are higher order in the incoming field, such as hyper-Raman scattering. Here we explain how to implement this time-dependent formalism within the dynamical mean field theory framework. The method is illustrated with applications to the Holstein-Hubbard model in the strong electron-phonon coupling regime. We demonstrate hyper-Raman scattering in measurements with strong probe fields and frequency mixing signals in the presence of a pump field and simulate the evolution of Stokes and anti-Stokes features after photoexcitations of metallic and Mott insulating systems.
The real-time dynamics of interacting electrons out of equilibrium contains detailed microscopic information about electronically correlated materials, which can be read out with time-resolved optical spectroscopy. The reflectivity that is typically measured in pump-probe experiments is related to the nonequilibrium optical conductivity. We show how to express this quantity in terms of real-time Green's functions using dynamical mean-field theory. As an application we study the electrical response of the Falicov-Kimball model during the ultrafast buildup of the gapped phase at large interaction.
Ultrafast characterization and control of many-body interactions and elementary excitations are critical to understanding and manipulating emergent phenomena in strongly correlated systems. In particular, spin interaction plays an important role in unconventional superconductivity, but efficient tools for probing spin dynamics, especially out of equilibrium, are still lacking. To address this question, we develop a theory for nonresonant time-resolved Raman scattering, which can be a generic and powerful tool for nonequilibrium studies. We also use exact diagonalization to simulate the pump-probe dynamics of correlated electrons in the square-lattice single-band Hubbard model. Different ultrafast processes are shown to exist in the time-resolved Raman spectra and dominate under different pump conditions. For high-frequency and off-resonance pumps, we show that the Floquet theory works well in capturing the softening of bimagnon excitation. By comparing the Stokes and anti-Stokes spectra, we also show that effective heating dominates at small pump fluences, while a coherent many-body effect starts to take over at larger pump amplitudes and frequencies on resonance to the Mott gap. Time-resolved Raman scattering thereby provides the platform to explore different ultrafast processes and design material properties out of equilibrium.
We present a generalized dynamical mean-field approach for the nonequilibrium physics of a strongly correlated system in the presence of a time-dependent external field. The Keldysh Green's function formalism is used to study the nonequilibrium problem. We derive a closed set of self-consistency equations in the case of a driving field with frequency Omega and wave vector q. We present numerical results for the local frequency-dependent Green's function and the self-energy for different values of the field amplitude in the case of a uniform external field using the iterated perturbation theory. In addition, an expression for the frequency-dependent optical conductivity of the Hubbard model with a driving external field is derived.