Broadening of the Derivative Discontinuity in Density Functional Theory

TL;DR

This paper investigates how the derivative discontinuity in density functional theory broadens in a quantum dot model with particle number fluctuations, revealing the influence of contact-induced level broadening and Kondo-like fluctuations.

Contribution

It provides a detailed analysis of the factors controlling derivative discontinuity broadening in a correlated quantum system, highlighting the role of the ratio mma/U and Kondo fluctuations.

Findings

DD-broadening is controlled by mma/U ratio

Kondo fluctuations can double the DD-broadening

Broadening increases with particle number fluctuations

Abstract

We clarify an important aspect of density functional theories, the broadening of the derivative discontinuity (DD) in a quantum system, with fluctuating particle number. Our focus is on a correlated model system, the single level quantum dot in the regime of the Coulomb blockade. We find that the DD-broadening is controlled by the small parameter $\Gamma/U$, where $\Gamma$ is the level broadening due to contacting and $U$ is a measure of the charging energy. Our analysis suggests, that Kondoesque fluctuations have a tendency to increase the DD-broadening, in our model by a factor of two.