  The effects of the electron-phonon interaction on optical excitations can be
understood in terms of exciton-phonon coupling, and require a careful treatment
in low-dimensional materials with strongly bound excitons or strong
electron-hole interaction in general. Through phonon absorption and emission
processes, the optically accessible excitons are scattered into otherwise
optically dark finite-momentum exciton states. We derive a practical expression
for the phonon-induced term of the exciton self-energy (denoted as the
exciton-phonon self-energy) that gives the temperature dependence of the
optical transition energies and their lifetime broadening resulting from the
exciton's interaction with the phonons. We illustrate this theory on a
two-dimensional model, and show that our expression for the exciton-phonon
self-energy differs qualitatively from previous expressions found in the
literature that neglect the exciton binding or electron-hole correlations.
