Correlation energy of a two-dimensional electron gas from static and dynamic exchange-correlation kernels

TL;DR

This paper computes the correlation energy of a 2D electron gas using various exchange-correlation kernels, analyzing the importance of their frequency and wave number dependencies, and comparing the effectiveness of different approximations.

Contribution

It provides a detailed analysis of the roles of static and dynamic exchange-correlation kernels in calculating 2D electron gas correlation energy, highlighting the importance of consistency with pair distribution functions.

Findings

Kernel consistency with pair distribution functions is crucial.

Nonlocality in time of the kernel has minor impact on correlation energy.

Adiabatic Local Density Approximation performs better in 2D than in 3D.

Abstract

We calculate the correlation energy of a two-dimensional homogeneous electron gas using several available approximations for the exchange-correlation kernel $f_{\rm xc}(q,\omega)$ entering the linear dielectric response of the system. As in the previous work of Lein {\it et al.} [Phys. Rev. B {\bf 67}, 13431 (2000)] on the three-dimensional electron gas, we give attention to the relative roles of the wave number and frequency dependence of the kernel and analyze the correlation energy in terms of contributions from the $(q, i\omega)$ plane. We find that consistency of the kernel with the electron-pair distribution function is important and in this case the nonlocality of the kernel in time is of minor importance, as far as the correlation energy is concerned. We also show that, and explain why, the popular Adiabatic Local Density Approximation performs much better in the two-dimensional case than in the three-dimensional one.