Phonon spectral function of the Holstein polaron

TL;DR

This paper analyzes the phonon spectral function of the one-dimensional Holstein model using analytical approximations and numerical methods, revealing different physical behaviors in adiabatic and anti-adiabatic regimes.

Contribution

It provides a combined analytical and numerical study of the phonon spectral function in the Holstein model, highlighting regime-dependent physics and validating approximations with cluster-based numerical results.

Findings

Analytical self-energy calculations describe phonon spectral features.

Comparison with numerical cluster methods confirms analytical results.

Accurate results obtained in intermediate-coupling regime.

Abstract

The phonon spectral function of the one-dimensional Holstein model is obtained within weak and strong-coupling approximations based on analytical self-energy calculations. The characteristic excitations found in the limit of small charge-carrier density are related to the known (electronic) spectral properties of Holstein polarons such as the polaron band dispersion. Particular emphasis is laid on the different physics occurring in the adiabatic and anti-adiabatic regimes, respectively. Comparison is made with a cluster approach exploiting exact numerical results on small systems to yield an approximation for the thermodynamic limit. This method, similar to cluster perturbation theory, confirms the analytical findings, and yields accurate results also in the intermediate-coupling regime.