Density functional theory for a model quantum dot: Beyond the local-density approximation

TL;DR

This paper evaluates various density functional theory approaches for modeling quantum dots, highlighting their accuracy limitations and proposing combined methods that improve results, especially for intermediate interactions, but also questioning the predictive power for conductance.

Contribution

The study introduces a combined approach of exact diagonalization and density functional theory that enhances accuracy for quantum dot properties beyond local-density approximation.

Findings

Optimized effective potential method works well for weak interactions.

Combined small-cluster exact diagonalization and DFT yields accurate results for intermediate interactions.

Static DFT often fails to predict the exact linear conductance correctly.

Abstract

We study both static and transport properties of model quantum dots, employing density functional theory as well as (numerically) exact methods. For the lattice model under consideration the accuracy of the local-density approximation generally is poor. For weak interaction, however, accurate results are achieved within the optimized effective potential method, while for intermediate interaction strengths a method combining the exact diagonalization of small clusters with density functional theory is very successful. Results obtained from the latter approach yield very good agreement with density matrix renormalization group studies, where the full Hamiltonian consisting of the dot and the attached leads has to be diagonalized. Furthermore we address the question whether static density functional theory is able to predict the exact linear conductance through the dot correctly - with, in general, negative answer.