Density-functional theory and the v-representability problem for model strongly correlated electron systems

TL;DR

This paper reexamines the application of density-functional theory to strongly correlated Hubbard models, revealing that the electron density in such systems cannot be accurately represented by noninteracting Kohn-Sham electrons due to correlation effects.

Contribution

It provides a formal framework for applying density-functional theory to strongly correlated systems and demonstrates the limitations of v-representability through numerical analysis.

Findings

Density-functional theory is formally applicable to strongly correlated systems.

Kohn-Sham electrons cannot reproduce correlation-induced localization.

Electron density in these systems is not noninteracting v representable.

Abstract

Inspired by earlier work on the band-gap problem in insulators, we reexamine the treatment of strongly correlated Hubbard-type models within density-functional theory. In contrast to previous studies, the density is fully parametrized by occupation numbers and overlap of orbitals centered at neighboring atomic sites, as is the local potential by the hopping matrix. This corresponds to a good formal agreement between density-functional theory in real space and second quantization. It is shown that density-functional theory is formally applicable to such systems and the theoretical framework is provided. The question of noninteracting v representability is studied numerically for finite one-dimensional clusters, for which exact results are available, and qualitatively for infinite systems. This leads to the conclusion that the electron density corresponding to interacting systems of the type studied here is in fact not noninteracting v representable because the Kohn-Sham electrons are unable to reproduce the correlation-induced localization correctly.