Spectral function of electron-phonon models by cluster perturbation theory

TL;DR

This paper employs cluster perturbation theory combined with the Lanczos method to accurately compute the spectral function of the Holstein polaron in one and two dimensions, reducing finite-size effects and validating results against exact data.

Contribution

It introduces a reliable computational approach using small clusters for spectral functions in electron-phonon models, improving upon finite-size limitations of previous methods.

Findings

Method yields accurate spectral functions with small clusters.

Results agree with exact data and previous approximations.

Reduces finite-size effects significantly.

Abstract

Cluster perturbation theory in combination with the Lanczos method is used to compute the one-electron spectral function of the Holstein polaron in one and two dimensions. It is shown that the method allows reliable calculations using relatively small clusters, and at the same time significantly reduces finite-size effects. Results are compared with exact data and the relation to existing work is discussed. We also use a strong-coupling perturbation theory--equivalent to the Hubbard I approximation--to calculate the spectral function of the quarter-filled Holstein model of spinless fermions, starting from the exact atomic-limit Green function. The results agree well with previous calculations within the many-body coherent potential approximation.