Converging toward a practical solution of the Holstein molecular crystal model

Abstract

We present selected results for the Holstein molecular crystal model in one space dimension as determined by the Global–Local variational method, including complete polaron energy bands, ground state energies, and effective masses. We juxtapose our results with specific comparable results of numerous other methodologies of current interest, including quantum Monte Carlo, cluster diagonalization, dynamical mean field theory, density matrix renormalization group, semiclassical analysis, weak-coupling perturbation theory, and strong-coupling perturbation theory. Taken as a whole, these methodologies are mutually confirming and provide a comprehensive and quantitatively accurate description of polaron properties in essentially any regime. In particular, this comparison confirms the Global–Local variational method as being highly accurate over a wide range of the polaron parameter space, from the nonadiabatic limit to the extremes of high adiabaticity, from weak coupling through intermediate coupling to strong coupling.