Dynamic exchange-correlation potentials for the electron gas in dimensionality D=3 and D=2
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.
Cite
@article{arxiv.cond-mat/9807085,
title = {Dynamic exchange-correlation potentials for the electron gas in dimensionality D=3 and D=2},
author = {R. Nifosi' and S. Conti and M. P. Tosi},
journal= {arXiv preprint arXiv:cond-mat/9807085},
year = {2008}
}
Comments
13 pages, 11 figures included. Accepted for publication in Phys. Rev. B