CONVERGING TOWARD A PRACTICAL SOLUTION OF THE HOLSTEIN MOLECULAR-CRYSTAL MODEL

We present selected results for the Holstein molecular crystal model i n one space dimension as determined by the Global-Local variational me thod, including complete polaron energy bands, ground state energies, and effective masses. We juxtapose our results with specific comparabl e results of numerous other methodologies of current interest, includi ng quantum Monte Carlo, cluster diagonalization, dynamical mean field theory, density matrix renormalization group, semiclassical analysis, weak-coupling perturbation theory, and strong-coupling perturbation th eory. Taken as a whole, these methodologies an mutually confirming and provide a comprehensive and quantitatively accurate description of po laron properties in essentially any regime. In particular, this compar ison confirms the Global-Local variational method as being highly accu rate over a wide range of the polaron parameter space, from the nonadi abatic limit to the extremes of high adiabaticity, from weak coupling through intermediate coupling to strong coupling. (C) 1998 American In stitute of Physics. [S0021-9606(98)51140-3].