The derivative discontinuity in the strong-interaction limit of density functional theory

TL;DR

This paper extends the strong-interaction limit of density functional theory to open systems with fluctuating particles, accurately capturing derivative discontinuities and improving understanding of strongly correlated electronic systems.

Contribution

It generalizes the strong-interaction limit functional to open systems, providing exact features for strongly-interacting systems and supporting the existence of the derivative discontinuity without standard assumptions.

Findings

Accurately captures the step-like structure of Kohn-Sham eigenvalues.

Shows a smoothened derivative discontinuity at finite correlation regimes.

Provides independent support for the existence of the derivative discontinuity.

Abstract

We generalize the exact strong-interaction limit of the exchange-correlation energy of Kohn-Sham density functional theory to open systems with fluctuating particle numbers. When used in the self-consistent Kohn-Sham procedure on strongly-interacting systems, this functional yields exact features crucial for important applications such as electronic transport. In particular, the step-like structure of the highest-occupied Kohn-Sham eigenvalue is very well captured, with accurate quantitative agreement with exact many-body chemical potentials. Whilst it can be shown that a sharp derivative discontinuity is only present in the infinitely strong-correlated limit, at finite correlation regimes we observe a slightly-smoothened discontinuity, with qualitative and quantitative features that improve with increasing correlation. From the fundamental point of view, our results obtain the derivative discontinuity without making the assumptions used in its standard derivation, offering independent support for its existence.