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 pi, 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 pi-ton. Here we add the pi-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 pi-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 pi-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 pi-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.