Polaron Mass and Electron-Phonon Correlations in the Holstein Model

TL;DR

This paper investigates the Holstein model using a strong coupling perturbative method that includes retardation effects, revealing the polaron crossover, mass enhancement, and conditions for light polarons across different dimensions.

Contribution

It introduces a perturbative approach accounting for phonon dispersion, providing new insights into polaron mass, crossover behavior, and electron-phonon correlations in various dimensions.

Findings

Polaron crossover occurs in all dimensions for adiabatic regimes.

Phonon dispersion smooths the polaron crossover.

Conditions for light polarons are identified in 2D and 3D.

Abstract

The Holstein Molecular Crystal Model is investigated by a strong coupling perturbative method which, unlike the standard Lang-Firsov approach, accounts for retardation effects due to the spreading of the polaron size. The effective mass is calculated to the second perturbative order in any lattice dimensionality for a broad range of (anti)adiabatic regimes and electron-phonon couplings. The crossover from a large to a small polaron state is found in all dimensionalities for adiabatic and intermediate adiabatic regimes. The phonon dispersion largely smooths such crossover which is signalled by polaron mass enhancement and on site localization of the correlation function. The notion of self-trapping together with the conditions for the existence of light polarons, mainly in two- and three-dimensions, are discussed. By the imaginary time path integral formalism I show how non local electron-phonon correlations, due to dispersive phonons, renormalize downwards the {\it e-ph} coupling justifying the possibility for light and essentially small 2D Holstein polarons.