Transforming nonlocality into frequency dependence: a shortcut to spectroscopy

TL;DR

This paper introduces an exact method to derive local, real, and dynamical potentials for calculating electronic spectra directly, simplifying the process and providing insights into frequency dependence and nonlocal effects.

Contribution

It presents a novel approach to construct effective local potentials for electronic spectra, reducing complexity and enhancing understanding of frequency dependence in photoemission and absorption.

Findings

Derived a local, dynamical potential for spectral functions

Applied method to sodium and aluminium as homogeneous electron gases

Provided a short derivation of a known kernel for spectra description

Abstract

Measurable spectra are theoretically very often derived from complicated many-body Green's functions. In this way, one calculates much more information than actually needed. Here we present an in principle exact approach to construct effective potentials and kernels for the direct calculation of electronic spectra. In particular, the potential that yields the spectral function needed to describe photoemission turns out to be dynamical but {\it local} and {\it real}. As example we illustrate this ``photoemission potential'' for sodium and aluminium, modelled as homogeneous electron gas, and discuss in particular its frequency dependence stemming from the nonlocality of the corresponding self-energy. We also show that our approach leads to a very short derivation of a kernel that is known to well describe absorption and energy-loss spectra of a wide range of materials.