Nonequilibrium evolution of the optical conductivity of the weakly interacting Hubbard model: Drude response and π-ton type vertex corrections

The optical conductivity contains information about energy absorption and the underlying physical processes. In finite-dimensional systems, vertex corrections to the bare bubble need to be considered, which is a computationally challenging task. Recent numerical studies showed that in the weak-coupling limit, near an ordering instability with wave-vector π, the vertical ladder describing particle-hole pairs interacting via the exchange of this wave vector becomes the dominant vertex correction. The corresponding Maki-Thompson-like diagram has been dubbed π-ton. Here we add the π-ton ladder vertex correction to dynamical mean-field theory estimates of the optical conductivity. By performing calculations on the Kadanoff-Baym contour, we reveal the characteristic spectral signatures of the π-tons and their evolution under nonequilibrium conditions. We consider interaction quenches of the weakly correlated Hubbard model near the antiferromagnetic phase boundary and analyze the evolution of the Drude and π-ton features. While the bubble contribution to the optical conductivity is found to thermalize rapidly, after some oscillations with frequencies related to the local spectral function, the π-ton contribution exhibits a slower evolution. We link this observation to the prethermalization phenomenon which has been previously studied in weakly interacting, quenched Hubbard models.