Electron-phonon correlations, polaron size, and the nature of the self-trapping transition

We analyze electron-phonon correlation functions measured in 1D polaron gro und states of the Holstein Hamiltonian using the Global-Local variational m ethod. The spatial collapse of electron-phonon col-relations is found to oc cur in concert with transition behavior in other polaron properties, provid ing mutually confirming evidence for a self-trapping Line in 1D. The spacia l extent of electron-phonon correlations is used to quantify polaron size, and is analyzed over a wide range of parameters. Distinct scaling behaviors are found to be characteristic of the region below the self-trapping trans ition and above it, contrary to some widely-held expectations and leading n aturally to the notion of the polaron size as an order parameter for a self -trapping transition that becomes critical in the adiabatic limit. (C) 2000 Published by Elsevier Science B.V. All rights reserved.