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

Abstract

We analyze electron–phonon correlation functions measured in 1D polaron ground states of the Holstein Hamiltonian using the Global–Local variational method. The spatial collapse of electron–phonon correlations is found to occur in concert with transition behavior in other polaron properties, providing mutually confirming evidence for a self-trapping line in 1D. The spatial 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 transition and above it, contrary to some widely-held expectations and leading naturally to the notion of the polaron size as an order parameter for a self-trapping transition that becomes critical in the adiabatic limit.