Testing the nonlocal kinetic energy functional of an inhomogeneous, two-dimensional degenerate Fermi gas within the average density approximation

TL;DR

This paper evaluates the average density approximation (ADA) for the kinetic energy functional in a 2D Fermi gas, showing it performs well across various potentials and particle numbers, with the Thomas-Fermi approximation also surprisingly effective.

Contribution

The paper provides a detailed comparison of ADA-based kinetic energy calculations with exact Kohn-Sham results, demonstrating ADA's accuracy without fitting parameters in 2D Fermi gases.

Findings

ADA performs well across different confinement potentials.

Thomas-Fermi approximation yields good global kinetic energy results.

ADA accurately captures local and global properties of the 2D Fermi gas.

Abstract

In a recent paper [Phys.~Rev.~A {\bf 89}, 022503 (2014)], the average density approximation (ADA) was implemented to develop a parameter-free, nonlocal kinetic energy functional to be used in the orbital-free density-functional theory of an inhomogenous, two-dimensional (2D), Fermi gas. In this work, we provide a detailed comparison of self-consistent calculations within the ADA with the exact results of the Kohn-Sham density-functional theory, and the elementary Thomas-Fermi (TF) approximation. We demonstrate that the ADA for the 2D kinetic energy functional works very well under a wide variety of confinement potentials, even for relatively small particle numbers. Remarkably, the TF approximation for the kinetic energy functional, {\em without any gradient corrections}, also yields good agreement with the exact kinetic energy for all confining potentials considered, although at the expense of the spatial and kinetic energy densities exhibiting poor point-wise agreement, particularly near the TF radius. Our findings illustrate that the ADA kinetic energy functional yields accurate results for {\em both} the local and global equilibrium properties of an inhomogeneous 2D Fermi gas, without the need for any fitting parameters.