Quasi-particle characteristics of the one-dimensional polaron

TL;DR

This paper investigates the fundamental properties of the one-dimensional polaron across different coupling regimes, providing improved estimates for ground-state energy and effective mass, and analyzing higher-order corrections beyond Gaussian approximation.

Contribution

It derives explicit expressions for the polaron's ground-state energy and effective mass, and improves upon Feynman's estimates by including non-Gaussian corrections.

Findings

Gaussian approximation yields a lower bound for self energy.

Higher-order corrections do not significantly alter results.

Improved estimates for energy and mass across coupling regimes.

Abstract

The main quasi-particle characteristics of the one-dimensional polaron are estimated within and beyond the most general Gaussian approximation at arbitrary electron-phonon coupling. We have derived explicitly the ground-state energy and the effective mass in the weak- and strong-coupling regimes. For arbitrary coupling, the Gaussian leading-order term of the polaron self energy improves the corresponding Feynman estimate and represents the lowest upper bound available. We have calculated the next non-Gaussian corrections. Taking into account systematically higher-order corrections does not perturb considerably the obtained results.