Polaron formation for non-local electron-phonon coupling: A variational wave-function study

We introduce a variational wave function to study the polaron formation when the electronic transfer integral depends on the relative displacement between nearest-neighbor sites giving rise to a nonlocal electron-phonon coupling with optical phonon modes. We characterize the polaron crossover by analyzing ground-state properties such as the energy, the electron-lattice correlation function, the average phonon occupation, and the quasiparticle spectral weight. Variational results are found in good agreement with numerical exact diagonalization of small clusters,and follow the correct perturbative result at weak coupling. We determine the polaronic phase diagram and we find that the tendency towards strong localization is hindered from the pathological sign change of the effective next-nearest-neighbor hopping.