Polaron formation for a non-local electron-phonon coupling: A variational wave-function study

TL;DR

This study introduces a variational wave-function approach to analyze polaron formation with non-local electron-phonon coupling, providing insights into ground state properties and phase diagram, and comparing results with perturbative and numerical methods.

Contribution

The paper presents a novel variational wave-function method for non-local electron-phonon interactions, extending understanding of polaron properties beyond local coupling models.

Findings

Good agreement with perturbative and numerical results

Identification of the polaronic phase diagram

Localization tendency hindered by sign change in effective hopping

Abstract

We introduce a variational wave-function to study the polaron formation when the electronic transfer integral depends on the relative displacement between nearest-neighbor sites giving rise to a non-local electron-phonon coupling with optical phonon modes. We analyze the ground state properties such as the energy, the electron-lattice correlation function, the phonon number and the spectral weight. Variational results are found in good agreement with analytic weak-coupling perturbative calculations and exact numerical diagonalization of small clusters. We determine the polaronic phase diagram and we find that the tendency towards strong localization is hindered from the pathological sign change of the effective next-nearest-neighbor hopping.