Green's Function Approach to Exciton-Phonon Interactions

The system of a tightly bound exciton which is weakly coupled to phonons is treated by means of manybody Green's functions. Relevance of the formalism for the calculation of absorption and emission spectra, quasiparticle properties, lattice distortion, and exciton propagation is established. A variational technique is found useful for deriving formal relationships. Evaluations are carried out for an approximate Hamiltonian representing excitons in a one-dimensional lattice; both Einstein-model phonons and one-dimensional acoustic phonons are investigated. Approximations include a one-phonon approximation and, for many-phonon processes, the replacement of the exciton-phonon vertex function $\Gamma$ by unity. The relation of these approximations to perturbation theory is assessed in specific cases. Finite-temperature calculations performed apply to excitons whose energies are large compared to $\kappa T$. Among the results is the conclusion that the interacting exciton is not merely "renormalized"; instead, as in the case of electron-phonon interactions, the spectrum of excitations includes many diverse quasiparticle modes and other complex structure.