Photoexcitations in the Hubbard model: Generalized Loschmidt amplitude analysis of impact ionization in small clusters

We study photoexcitations in small Hubbard clusters of up to 12 sites. After the electric field pulse some of these clusters show an increase of the double occupation through impact ionization. We treat the time-dependent electromagnetic field classically and calculate time evolution by exact diagonalization. As a tool for better analyzing the out-of-equilibrium dynamics, we generalize the Loschmidt amplitude. In this way we are able to resolve which many-body energy eigenstates are responsible for impact ionization and which ones show pronounced changes in the double occupation and spin energy. Our analysis reveals that the increase of spin energy is of little importance for impact ionization. We further demonstrate that, for one-dimensional chains, the optical conductivity has a characteristic peak structure originating solely from vertex corrections.