Photoexcitations in the Hubbard model -- generalized Loschmidt amplitude analysis of impact ionization in small clusters

TL;DR

This paper investigates photoinduced impact ionization in small Hubbard clusters using generalized Loschmidt amplitude analysis, revealing the roles of many-body states and the insignificance of spin energy loss.

Contribution

It introduces a generalized Loschmidt amplitude to analyze out-of-equilibrium dynamics and impact ionization in small Hubbard clusters, providing new insights into the involved many-body states.

Findings

Impact ionization increases double occupation in some clusters.

Loss of spin energy is not crucial for impact ionization.

Optical conductivity in 1D chains shows a peak from vertex corrections.

Abstract

We study photoexcitations in small Hubbard clusters of up to 12 sites, some of which show an increase of the double occupation after the electric field pulse through impact ionization. Here, the time-dependent electromagnetic field is introduced through a Peierls substitution and the time evolution is calculated by exact diagonalization with commutator-free Magnus integrators. As a tool to better analyze the out-of-equilibrium dynamics, we generalize the Loschmidt amplitude. This way, we are able to resolve which many-body energy eigenstates are responsible for impact ionization and which show pronounced changes in the double occupation and spin energy. This analysis reveals that the loss 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.