Adiabatic theory of the polaron 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 μ → − ∞ the ground state does not have the adiabatic deformation and the spectral function is defined by the standard perturbation theory. In this limit we use the diagram technique in order to formulate an integral equation for the renormalized vertex. The spectral function was evaluated by solving the Dyson’s equation for the self-energy with the renormalized vertex. The moments of the spectral function satisfy the exact sum rules up to the 7th 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.