  We present a generic procedure for quantifying the interplay of electronic
and lattice degrees of freedom in photo-doped insulators through a comparative
analysis of theoretical many-body simulations and time- and angle-resolved
photoemission spectroscopy (TR-ARPES) of the transient response of the
candidate excitonic insulator Ta2NiSe5. Our analysis demonstrates that the
electron-electron interactions dominate the electron-phonon ones. In
particular, a detailed analysis of the TRARPES spectrum enables a clear
separation of the dominant broadening (electronic lifetime) effects from the
much smaller bandgap renormalization. Theoretical calculations show that the
observed strong spectral broadening arises from the electronic scattering of
the photo-excited particle-hole pairs and cannot be accounted for in a model in
which electron-phonon interactions are dominant. We demonstrate that the
magnitude of the weaker subdominant bandgap renormalization sensitively depends
on the distance from the semiconductor/semimetal transition in the
high-temperature state, which could explain apparent contradictions between
various TR-ARPES experiments. The analysis presented here indicates that
electron-electron interactions play a vital role (although not necessarily the
sole one) in stabilizing the insulating state.
