Small polaron formation in the Holstein and Su-Schrieffer-Heeger models: The criteria from analytic and numerical analyses

TL;DR

This paper explores the conditions under which polarons form in the Holstein and SSH models, combining analytic and numerical methods to identify key criteria for polaronic regimes.

Contribution

It introduces combined analytic and numerical criteria for polaron formation in two fundamental models, clarifying their physical origins.

Findings

Different parameter criteria for polaron formation in the two models

Polaron formation involves large ionic displacement and energy gain surpassing kinetic loss

Unified physical understanding of polarons in both models

Abstract

We investigate the conditions leading to polaron formation for a single electron interacting with dispersionless optical phonons within the Holstein and the Su-Schrieffer-Heeger models. Both from analytic perturbation theory and exact numerical diagonalization of small clusters, we find different criteria for the model parameters ruling the setting in of the polaronic regime. We also illustrate the common physical origin of polarons in the two models as arising from the simultaneous fulfilling of two conditions: A sizable ionic displacement and a lattice deformation energy gain larger that the loss in the bare electron kinetic energy.