Dynamic exchange-correlation potentials for the electron gas in dimensionality D=3 and D=2

TL;DR

This paper develops a dynamical local approximation for exchange-correlation potentials in the electron gas, analyzing their spectra in 2D and 3D, and revealing how plasmon excitations influence the kernel's behavior.

Contribution

It introduces a new approximate decoupling method for the current-density response in electron gases, accounting for two-electron-hole pair excitations and including exchange effects phenomenologically.

Findings

Identification of a sharp minimum at twice the plasma frequency in 3D.

Observation of a broad spectral peak in 2D due to plasmon dispersion.

Numerical spectra fitted to simple analytic functions.

Abstract

Recent progress in the formulation of a fully dynamical local approximation to time-dependent Density Functional Theory appeals to the longitudinal and transverse components of the exchange and correlation kernel in the linear current-density response of the homogeneous fluid at long wavelength. Both components are evaluated for the electron gas in dimensionality D=3 and D=2 by an approximate decoupling in the equation of motion for the current density, which accounts for processes of excitation of two electron-hole pairs. Each pair is treated in the random phase approximation, but the role of exchange and correlation is also examined; in addition, final-state exchange processes are included phenomenologically so as to satisfy the exactly known high-frequency behaviours of the kernel. The transverse and longitudinal spectra involve the same decay channels and are similar in shape. A two-plasmon threshold in the spectrum for two-pair excitations in D=3 leads to a sharp minimum in the real part of the exchange and correlation kernel at twice the plasma frequency. In D=2 the same mechanism leads to a broad spectral peak and to a broad minimum in the real part of the kernel, as a consequence of the dispersion law of the plasmon vanishing at long wavelength. The numerical results have been fitted to simple analytic functions.