Missing derivative discontinuity of the exchange-correlation energy for attractive interactions: the charge Kondo effect

TL;DR

This paper reveals that for systems with attractive interactions, the exchange-correlation energy in ensemble DFT is convex without derivative discontinuities, impacting the modeling of the charge Kondo effect.

Contribution

It demonstrates the absence of derivative discontinuities in the XC potential for attractive interactions and emphasizes their importance in accurately describing the charge Kondo effect.

Findings

XC potential lacks discontinuity for odd N in the atomic limit

Discontinuity at even N is broadened with finite hybridizations

Proper inclusion of these properties reproduces charge-Kondo signatures

Abstract

We show that the energy functional of ensemble Density Functional Theory (DFT) [Perdew et al., Phys. Rev. Lett. 49, 1691 (1982)] in systems with attractive interactions is a convex function of the fractional particle number N and is given by a series of straight lines joining a subset of ground-state energies. As a consequence the exchange-correlation (XC) potential is not discontinuous for all N. We highlight the importance of this exact result in the ensemble-DFT description of the negative-U Anderson model. In the atomic limit the discontinuity of the XC potential is missing for odd N while for finite hybridizations the discontinuity at even N is broadened. We demonstrate that the inclusion of these properties in any approximate XC potential is crucial to reproduce the characteristic signatures of the charge-Kondo effect in the conductance and charge susceptibility.