Exact Kohn-Sham eigenstates versus quasiparticles in simple models of strongly correlated electrons

TL;DR

This paper derives exact density functionals and Kohn-Sham Hamiltonians for simple correlated-electron models, enabling comparison between DFT eigenstates and many-body quasiparticles, revealing both successes and limitations.

Contribution

It provides analytic expressions for the exact Kohn-Sham potentials in simple models, facilitating direct comparison with many-body quasiparticle spectra.

Findings

Kohn-Sham spectra capture many features of quasiparticle spectra

Some quasiparticle features are missing in Kohn-Sham spectra due to richer many-body phase space

Exact potentials are fully non-local, enabling detailed analysis

Abstract

We present analytic expressions for the exact density functional and Kohn-Sham Hamiltonian of simple tight-binding models of correlated electrons. These are the single- and double-site versions of the Anderson, Hubbard and spinless fermion models. The exact exchange and correlation potentials are fully non-local. The analytic expressions allow to compare the Kohn-Sham eigenstates of exact density functional theory with the many-body quasi-particle states of these correlated-electron systems. The exact Kohn-Sham spectrum describes correctly many of the non-trivial features of the many-body quasi-particle spectrum, as for example the precursors of the Kondo peak. However, we find that some pieces of the quasi-particle spectrum are missing because the many-body phase-space for electron and hole excitations is richer.