The weak, the large, and the empty: bringing order to concepts of spatial coherence in the Holstein polaron

We investigate polaron shape and size using electron-phonon correlation fun ctions measured in 1D polaron ground states of the Holstein Hamiltonian. We use the Global-Local variational method as our primary quantitative tool, calling upon weak- and strong-coupling perturbation theories to assist in t he interpretation of our results. The spatial extent of correlations is use d to quantify polaron size, and is analyzed over a wide range of parameters . Distinct scaling behaviors are found below the self-trapping transition a nd above it, leading naturally to the notion of the polaron size as an orde r parameter for a self-trapping transition that becomes critical in the adi abatic limit. The archetypical structure characterizing polaron shape and s ize below the self-trapping transition is found to differ significantly fro m what might be expected from certain widely held views. (C) 1999 Elsevier Science B.V. All rights reserved.