Exact weak-coupling radius of the Holstein polaron in one, two, and three dimensions

TL;DR

This paper uses weak-coupling perturbation theory to exactly compute the shape and size of Holstein polarons in one, two, and three dimensions, revealing limitations of the adiabatic approximation.

Contribution

It provides an exact leading-order calculation of the electron-phonon correlation function for Holstein polarons across different dimensions, including anisotropic cases.

Findings

Polaron width varies with direction and dimension.

Results challenge traditional adiabatic and self-trapping characterizations.

Discrepancies highlight breakdown of adiabatic approximation.

Abstract

We apply weak-coupling perturbation theory to the Holstein molecular crystal model in order to compute an electron-phonon correlation function characterizing the shape and size of the polaron lattice distortion in one, two, and three dimensions. This correlation function is computed exactly to leading order in the electron-phonon coupling constant, permitting a complete description of correlations in any dimension for both isotropic and arbitrarily anisotropic cases. Using this exact result, the width of the polaron is characterized along arbitrary directions. The width of the polaron thus determined disagrees in every dimension with some well-known characterizations of polarons, signalling in particular the breakdown of the adiabatic approximation and the characterizations of self-trapping associated with it.