Polaron Mass and Electron-Phonon Correlations in the Holstein Model

The Holstein Molecular Crystal Model is investigated by a strong coupling perturbative method which, unlike the standard Lang-Firsov approach, accounts for retardation effects due to the spreading of the polaron size. The effective mass is calculated to the second perturbative order in any lattice dimensionality for a broad range of (anti) adiabatic regimes and electron-phonon couplings. The crossover from a large to a small polaron state is found in all dimensionalities for adiabatic and intermediate adiabatic regimes. The phonon dispersion largely smoothes such crossover which is signalled by polaron mass enhancement and on-site localization of the correlation function. The notion of self-trapping together with the conditions for the existence of light polarons, mainly in two-and three-dimensions, is discussed. By the imaginary time path integral formalism I show how nonlocal electron-phonon correlations, due to dispersive phonons, renormalize downwards the e-ph coupling justifying the possibility for light and essentially small 2D Holstein polarons.