Ground State of the Exciton-Phonon System

The ground state of a model exciton-phonon Hamiltonian is studied using variational techniques. A single-exciton band is considered in the tight-binding model; the exciton is coupled to Einstein phonons through a short-range linear interaction. We first verify that a variational wave function corresponding to simple displacements of the lattice coordinates (analogous to the Lee-Low-Pines wave function for the polaron) leads to an unphysical result: For strong exciton-phonon coupling the effective mass of the excitons depends discontinuously on the parameters of the Hamiltonian. We obtain an improved trial function by studying an exactly soluble problem: an exciton hopping between two sites and coupled to a phonon field. The new trial function allows distortion of the Gaussian form of the phonon wave function as well as displacement. Analogous trial functions are used to calculate the energy and effective mass for a one-dimensional lattice with nearest-neighbor exciton hopping. The results are a continuous effective mass and a substantial improvement of the ground-state energy over the Lee-Low-Pines trial function. Arguments are given that the qualitative behavior of the ground state is independent of the dimensionality of the lattice, so that the one-dimensional calculation performed here is adequate.