  We study the interplay of electron-electron and electron-phonon interactions
in the course of electron-hole bound state formation for gapped solid state
systems. Adapting the essentially approximation-free diagrammatic Monte Carlo
method for the calculation of the optical response, we discuss the absorption
of light in correlated electron-phonon systems for the whole interaction and
phonon frequency regimes. The spectral function obtained by analytical
continuation from the imaginary-time current-current correlation function
demonstrates the dressing of excitons by a phonon cloud when the coupling the
lattice degrees of freedom becomes increasingly important, where notable
differences show up between the adiabatic and anti-adiabatic cases.
