Adiabatic theory of the polaron spectral function

TL;DR

This paper develops an analytic adiabatic theory for the electron-phonon spectral function, covering different chemical potential regimes and including finite polaron density effects, with calculations satisfying sum rules up to the 5th moment.

Contribution

It introduces a comprehensive adiabatic spectral function framework for electrons coupled with phonons, including finite polaron density and sum rule evaluations.

Findings

Spectral function calculated up to fourth order in coupling constant.

Sum rules for moments are satisfied up to the 5th moment.

Finite polaron density introduces polaron-specific features in the spectral function.

Abstract

An analytic theory for the spectral function for electrons coupled with phonons is formulated in the adiabatic limit. In the case when the chemical potential is large and negative $\mu \to -\infty$ the ground state does not have the adiabatic deformation and the spectral function is defined by the standard perturbation theory. In this limit we present the spectral function calculated up to fourth order in the electron-phonon coupling constant which satisfies the sum rules up to the 5th moment. In the case when the chemical potential is pinned at the polaron binding energy the spectral function is defined by the ground state with a nonzero adiabatic deformation. We calculate the spectral function with the finite polaron density in the adiabatic limit. We also demonstrate how the sum rules for higher moments may be evaluated in the adiabatic limit. Contrary to the case of zero polaron density the spectral function with the finite polaron concentration has some contributions which are characteristic for polarons.