Polaron band formation in the Holstein model

TL;DR

This paper provides exact numerical results for the polaron band structure in the Holstein model, revealing how electron-phonon interactions influence quasiparticle properties in one and two dimensions.

Contribution

It introduces a precise numerical approach using Lanczos diagonalization to analyze polaron band formation, comparing with strong-coupling perturbation theory in 2D.

Findings

Renormalization of quasiparticle bandwidth by electron-phonon interaction

Detailed dispersion relations for polarons in 1D and 2D

Validation of perturbation theory results in 2D

Abstract

We present numerical exact results for the polaronic band structure of the Holstein molecular crystal model in one and two dimensions. The use of direct Lanczos diagonalization technique, preserving the full dynamics and quantum nature of phonons, allows us to analyze in detail the renormalization of both quasiparticle bandwidth and dispersion by the electron-phonon interaction. For the two-dimensional case some of our exact data are compared with the results obtained in the framework of a recently developed finite cluster strong-coupling perturbation theory.