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

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.

arXiv comment5 pages, 4 figures

References in corpus (13)

• Angle-resolved photoemission spectroscopy of the cuprate superconductors
• Perspective on density functional theory
• Understanding Band Gaps of Solids in Generalized Kohn-Sham Theory
• Nearsightedness of Electronic Matter
• How is the derivative discontinuity related to steps in the exact Kohn-Sham potential?
• Exact time-dependent density-functional potentials for strongly correlated tunneling electrons
• Origin of static and dynamic steps in exact Kohn-Sham potentials
• Approximations for many-body Green's functions: insights from the fundamental equations
• GW approximation with self-screening correction
• Nearsightedness of Electronic Matter in One Dimension
• Accuracy of electron densities obtained via Koopmans-compliant hybrid functionals
• The role of electron localization in density functionals
• $GW$ self-screening error and its correction using a local density functional

Cited by in corpus (5)

• Accurate Kohn-Sham auxiliary system from the ground state density of solids
• Exact exchange-correlation potentials for calculating the fundamental gap with a fixed number of electrons
• Insights into one-body density matrices using deep learning
• Accurate real-time evolution of electron densities and ground-state properties from generalized Kohn-Sham theory
• Exact expressions for the height of the interatomic step in the exchange-correlation potential from the derivative discontinuity of the energy