Electron-Phonon Correlations, Polaron Size, and the Nature of the Self-Trapping Transition

TL;DR

This paper investigates the self-trapping transition in 1D polarons by analyzing electron-phonon correlations, revealing a critical change in polaron size and behavior across the transition using variational methods.

Contribution

It introduces a novel analysis of electron-phonon correlations to characterize the self-trapping transition and proposes polaron size as an order parameter.

Findings

Electron-phonon correlations collapse at the transition.

Polaron size exhibits distinct scaling behaviors across the transition.

Polaron size acts as a critical order parameter in the adiabatic limit.

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.