# Advantageous nearsightedness of many-body perturbation theory contrasted with Kohn-Sham density functional theory

## TL;DR

This paper compares many-body perturbation theory and Kohn-Sham density functional theory, showing that MBPT avoids certain pathological features of KS potentials due to non-local self-energy effects, highlighting the advantages of self-energy-based methods.

## Contribution

It demonstrates that MBPT inherently avoids pathological features like spatial steps in potentials, unlike KS theory, due to the non-locality of the self-energy, providing insights for future method development.

## Key findings

- MBPT lacks the spatial step features of KS potentials.
- Non-local self-energy renders pathological behavior unnecessary.
- Kohn's nearsightedness concept is numerically demonstrated.

## Abstract

For properties of interacting electron systems, Kohn-Sham (KS) theory is often favored over many-body perturbation theory (MBPT) owing to its low computational cost. However, the exact KS potential can be challenging to approximate, for example in the presence of localized subsystems where the exact potential is known to exhibit pathological features such as spatial steps. By modeling two electrons, each localized in a distinct potential well, we illustrate that the step feature has no counterpart in MBPTs (including Hartree-Fock and GW) or hybrid methods involving Fock exchange because the spatial non-locality of the self-energy renders such pathological behavior unnecessary. We present a quantitative illustration of the orbital-dependent nature of the non-local potential, and a numerical demonstration of Kohn's concept of the nearsightedness for self energies, when two distant subsystems are combined, in contrast to the KS potential. These properties emphasize the value of self-energy-based approximations in developing future approaches within KS-like theories.