Calculating time-resolved A_1g electronic Raman scattering via a functional-derivative approach

In nonequilibrium, the vertex correction to the electronic Raman scattering response function is time-dependent and very challenging to compute. Depending on the symmetry of the experiment, the nonresonant Raman scattering cross-section can be determined solely from the bare (with no vertex correction) loop, and we have already found an analytical expression for it in the case of a B_1g symmetry channel [1] (when the incident and scattered light are polarized perpendicular to each other). Instead, for an A_1g symmetry channel, which involves the full symmetry of the lattice, we apply a functional-derivative method to numerically calculate both the bare and renormalized contributions to the nonresonant response function. We present our results for the spinless Falicov-Kimball model, which is solved exactly in nonequilibrium using dynamical mean-field theory. We show results for pump-probe experiments with different Coulomb interactions that range from metals to Mott insulators.