Spectral functions of the spinless Holstein model

TL;DR

This paper presents an analytical method for calculating spectral functions in the one-dimensional spinless Holstein model at finite charge-carrier concentrations, bridging weak and strong coupling regimes.

Contribution

It introduces a generalized Lang-Firsov transformation with a variational parameter to interpolate between coupling limits and relates polaron and electron spectral functions.

Findings

Spectral functions show distinct coherent and incoherent parts.

Results align with recent numerical many-polaron calculations.

Method effectively captures spectral evolution with model parameters.

Abstract

An analytical approach to the one-dimensional spinless Holstein model is proposed, which is valid at finite charge-carrier concentrations. Spectral functions of charge carriers are computed on the basis of self-energy calculations. A generalization of the Lang-Firsov canonical transformation method is shown to provide an interpolation scheme between the extreme weak- and strong-coupling cases. The transformation depends on a variationally determined parameterthat characterizes the charge distribution across the polaron volume. The relation between the spectral functions of polarons and electrons, the latter corresponding to the photoemission spectrum, is derived. Particular attention is paid to the distinction between the coherent and incoherent parts of the spectra, and their evolution as a function of band filling and model parameters. Results are discussed and compared with recent numerical calculations for the many-polaron problem.