Testing of two-dimensional local approximations in the current-spin and spin-density-functional theories

TL;DR

This paper evaluates local approximation methods in current-spin and spin-density-functional theories for quantum dots, comparing their accuracy against quantum Monte Carlo results and discussing the importance of vorticity dependence.

Contribution

It introduces a comparative analysis of local approximations in current-spin and spin-density-functional theories for quantum dots, highlighting the significance of vorticity dependence.

Findings

Different parametrizations vary in accuracy compared to quantum Monte Carlo.

Vorticity dependence is crucial in certain regimes.

Local approximations have limitations in modeling quantum dot energetics.

Abstract

We study a model quantum dot system in an external magnetic field by using both the spin-density-functional theory and the current-spin-density-functional theory. The theories are used with local approximations for the spin-density and the vorticity. The reliabilities of different parametrizations for the exchange-correlation functionals are tested by comparing the ensuing energetics with quantum Monte Carlo results. The limit where the vorticity dependence should be used in the exchange-correlation functionals is discussed.