A convergent perturbation method for the Holstein model and its application to the double exchange system

We look for an analytical method which can describe the Holstein model over the entire region of electron-phonon (e-ph) coupling strength. Considering a toy model of two sites the perturbation expansions axe developed for the Holstein Hamiltonian using different standard phonon bases. It is found th at the modified Lang Firsov phonon basis shows satisfactory convergence for almost the entire range of e-ph coupling from the antiadiabatic limit to t he intermediate range of hopping. This method is used to study the magnetic transition and the small to large polaron crossover in a double exchange m odel with e-ph interaction. Implications of the results in the context of m anganites are discussed.