Electron-hole attraction effect under time-dependent electric field within a generalized Landau-Zener model

The exchange term is a crucial term for first-principles electronic structure theories, leading to accurate prediction within hybrid-functional for density-functional theory and the most simple many-body effect as a term in the Hartree-Fock (HF) equation. This term is also crucial for the description of the electronically excited state, namely excitonic influence on dielectric function either due to bound- or unbound-excitons. In spite of its importance in photoabsorption spectra, the effect of the (screened) exchange term for nonlinear phenomena has not been investigated well because of severe calculation cost.
Higher energetic electron-hole pairs in high-order harmonic generation spectra are reported by using one-dimensional HF simulation, compared with an independent particle system[1].
The effect is totally from modulation of the mean-field via a density-matrix change to a self-consistent solution of the HF equation. We develop a much simpler model that has an electron-hole attraction term imitating the exchange term on the top of the Landau-Zener model to investigate the dynamical effect of electron-hole attraction. We have observed a pronounced gap renormalization by increasing the field strength.
[1] Takuya Ikemachi, et al., Phys. Rev. A 98 (2018) 023415.