Spectral function of the small polaron

TL;DR

This paper provides an exact calculation of the spectral functions for electrons and small polarons in a two-site Holstein model, revealing limitations of the Lang-Firsov approximation and highlighting the small polaron as a key excitation.

Contribution

It offers the first exact spectral function calculations for the two-site Holstein model, comparing them with the Lang-Firsov approximation.

Findings

Small polaron is a better fundamental excitation than the electron at intermediate coupling.

Lang-Firsov approximation fails to accurately predict the small polaron dispersion.

Exact spectral functions reveal detailed polaron behavior in the model.

Abstract

We compute exactly both the spectral function of the electron and of the small polaron for the two site Holstein model. We find that for intermediary coupling, the small polaron is a better fundamental excitation of the system than the electron. However, the Lang-Firsov approximation fails to predict the right dispersion relation for the small polaron.