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

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

1998-07-06

arxiv.org/abs/cond-mat/9807085v1

Phys.Rev.B58:12758,1998

Physics

Condensed Matter

13 pages, 11 figures included. Accepted for publication in Phys. Rev. B

Scientific paper

10.1103/PhysRevB.58.12758

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.

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