No-go theorem for the description of Mott phenomena with conventional Density Functional Theory methods

TL;DR

This paper proves a fundamental limitation of standard density functional theory (DFT) methods in accurately describing Mott-Hubbard phenomena in strongly correlated electron systems, highlighting the need for new approaches.

Contribution

It establishes a necessary condition for DFT to describe Mott behavior and demonstrates that common functionals fail this condition, proposing an analytic approximation to improve modeling.

Findings

Standard DFT functionals do not satisfy the necessary condition for Mott-Hubbard behavior.

An analytic approximation to the exchange-correlation potential is proposed.

The results suggest limitations of current DFT methods in strongly correlated systems.

Abstract

Density functional theory provides the most widespread framework for the realistic description of the electronic structure of solids, but the description of strongly-correlated systems has remained so far elusive. Here we consider a particular limit of electrons in a periodic ionic potential in which a one-band description becomes exact all the way from the weakly-correlated metallic regime to the strongly-correlated Mott-Hubbard regime. We provide a necessary condition a density functional should fulfill to describe Mott-Hubbard behavior and show that it is not satisfied by standard and widely used local, semilocal and hybrid functionals. We illustrate the condition in the case of a few-atom system and provide an analytic approximation to the exact exchange-correlation potential based on a variational wave function which shows explicitly the correct behavior providing a robust scheme to combine lattice and continuum methods.