Role of long-range coupling on the properties of single polarons in models with dual electron-phonon couplings

TL;DR

This study uses variational exact diagonalization to analyze how long-range electron-phonon couplings influence single polaron properties in models combining short-range off-diagonal and longer-range diagonal interactions, revealing high sensitivity to coupling range and form.

Contribution

It provides a detailed analysis of the impact of coupling range and form on polaron properties in dual electron-phonon models, highlighting the importance of these factors for experimental comparisons.

Findings

Strong sensitivity of polaron properties to the range of diagonal coupling.

Significant dependence on the specific form of the diagonal coupling.

Sensitivity persists even at large phonon frequencies.

Abstract

We use the Variational Exact Diagonalization to investigate the single polaron properties for four different dual models, combining a short-range off-diagonal (Peierls) plus a longer-range diagonal (Holstein or breathing-mode) coupling. This allows us to investigate the sensitivity of various polaron properties both to the range of the diagonal coupling and to the specific diagonal coupling chosen. We find strong sensitivity to the range for all duals models as the adiabatic limit is approached, however considerable sensitivity is observed for some quantities even for large phonon frequencies. Also, the strong dependence of the results on the specific form of the diagonal coupling is observed everywhere in the parameter space. Taken together, these results suggest that careful consideration must be given to the specific coupling and its proper range when quantitative comparisons with experiments are sought.