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.

Automated summary

In this study, we investigate photoexcitations in small Hubbard clusters and find that some clusters exhibit an increase in double occupation through impact ionization after an electric field pulse. By treating the electromagnetic field classically and using exact diagonalization, we are able to identify the many-body eigenstates responsible for impact ionization and observe pronounced changes in double occupation and spin energy. Our analysis shows that the increase in spin energy is not significant for impact ionization. We also demonstrate that the characteristic peak structure of the optical conductivity in one-dimensional chains is solely due to vertex corrections.