Green's and spectral functions of the small Frolich polaron

TL;DR

This paper derives and analyzes the spectral functions of the small Frohlich polaron using Green's functions and perturbation theory, revealing differences in spectral weight and mass renormalization relevant for oxides.

Contribution

It applies the Lang-Firsov transformation to derive Green's functions for the small Frohlich polaron, providing new insights into spectral weight and mass renormalization.

Findings

Coherent spectral weight (Z) and effective mass (Z') renormalization exponents differ significantly.

Numerical spectral functions show small coherent spectral weight in oxides.

Theoretical results align with Quantum Monte Carlo simulations.

Abstract

According to recent Quantum Monte Carlo simulations the small polaron theory is practically exact in a wide range of the long-range (Frohlich) electron-phonon coupling and adiabatic ratio. We apply the Lang-Firsov transformation to convert the strong-coupling term in the Hamiltonian into the form of an effective hopping integral and derive the single-particle Green's function describing propagation of the small Frohlich polaron. One and two dimensional spectral functions are studied by expanding the Green's function perturbatively. Numerical calculations of the spectral functions are produced. Remarkably, the coherent spectral weight (Z) and effective mass (Z') renormalisation exponents are found to be different with Z'>>Z, which can explain a small coherent spectral weight and a relatively moderate mass enhancement in oxides.