Holstein light quantum polarons

TL;DR

This paper investigates polaron formation in the Holstein model's intermediate regime using exact diagonalization, revealing how nonadiabatic and adiabatic effects influence polaron lightness and dynamics.

Contribution

It provides a detailed analysis of the crossover between self-trapped and free-particle behaviors, highlighting the balance of nonadiabatic and adiabatic effects in polaron motion.

Findings

Polaron motion is governed by a balance of nonadiabatic and adiabatic contributions.

Light polarons result from this fine balance, even in the intermediate regime.

Different behaviors of the lattice deformation field are characterized across coupling regimes.

Abstract

The polaron formation is investigated in the intermediate regime of the Holstein model by using an exact diagonalization technique for the one-dimensional infinite lattice. The numerical results for the electron and phonon propagators are compared with the nonadiabatic weak- and strong-coupling perturbation theories, as well as with the harmonic adiabatic approximation. A qualitative explanation of the crossover regime between the self-trapped and free-particle-like behaviors, not well-understood previously, is proposed. It is shown that a fine balance of nonadiabatic and adiabatic contributions determines the motion of small polarons, making them light. A comprehensive analysis of spatially and temporally resolved low-frequency lattice correlations that characterize the translationally invariant polaron states is derived. Various behaviors of the polaronic deformation field, ranging from classical adiabatic for strong couplings to quantum nonadiabatic for weak couplings, are discussed.