Long wavelength behavior of the dynamical spin-resolved local-field factor in a two-dimensional electron liquid

The high frequency limits of the singular component $A(\omega)$ of the small wavevector expansion of the longitudinal (L) and transverse (T) components of the spin-resolved exchange-correlation kernel tensor $f_{xc,\sigma \sigma'}^{L,T}(q,\omega)=-v(q)G_{\sigma \sigma'}^{L,T}(q,\omega)$ in a two-dimensional isotropic electron liquid with arbitrary spin polarization are studied. Here $G_{\sigma \sigma'}^{L,T}(q,\omega)$ is the spin-resolved local field factor, $v(q)$ is the Coulomb interaction in momentum space, and $\sigma$ denotes spin. Particularly, the real part of $A(\omega)$ is found to be logarithmically divergent at large $\omega$. the large wavevetor structure of the corresponding spin-resolved static structure factor is also established

Static dielectric function with exact exchange contribution in the electron liquid

The exchange contribution, $\Pi_1 ({\bf k}, 0)$, to the static dielectric function in the electron liquid is evaluated exactly. Expression for it is derived analytically in terms of one quadrature. The expression, as presented in Eq. (3) in the Introduction, turns out to be very simple. A fully explicit expression (with no more integral in it) for $\Pi_1 ({\bf k}, 0)$ is further developed in terms of series. Equation (3) is proved to be equal to the expression obtained before under some mathematical assumption by Engel and Vosko, thus in the meanwhile putting the latter on a rigorous basis. The expansions of $\Pi_1 ({\bf k}, 0)$ at the wavectors of $k=0$, $k=2k_F$, and at limiting large $k$ are derived. The results all verify those obtained by Engel and Vosko.Comment: 15 page

Asymptotic near nucleus structure of the electron-interaction potential in local effective potential theories

In local effective potential theories of electronic structure, the electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and correlation-kinetic effects, are all incorporated in the local electron-interaction potential $v_{ee}({\bf r})$. In previous work, it has been shown that for spherically symmetric or sphericalized systems, the asymptotic near nucleus expansion of this potential is $v_{ee}(r) = v_{ee}(0) + \beta r + O(r^2)$, with $v_{ee}(0)$ being finite. By assuming that the Schr\"odinger and local effective potential theory wave functions are analytic near the nucleus of atoms, we prove the following via Quantal density functional theory (Q-DFT): (i) correlations due to the Pauli principle and Coulomb correlations do not contribute to the linear structure; (ii) these Pauli and Coulomb correlations contribute quadratically; (iii) the linear structure is {\em solely} due to correlation-kinetic effects, the contributions of these effects being determined analytically. We also derive by application of adiabatic coupling constant perturbation theory via Q-DFT (iv) the asymptotic near nucleus expansion of the Hohenberg-Kohn-Sham theory exchange $v_x({\bf r})$ and correlation $v_c({\bf r})$ potentials. These functions also approach the nucleus linearly with the linear term of $v_x({\bf r})$ being {\em solely} due to the lowest-order correlation kinetic effects, and the linear term of $v_c({\bf r})$ being due {\em solely} to the higher-order correlation kinetic contributions. The above conclusions are equally valid for systems of arbitrary symmetry, provided spherical averages of the properties are employed.Comment: 9 pages. Accepted for publication in Phys. Rev.

Spin dynamics from time-dependent spin density-functional theory

We derive the spin-wave dynamics of a magnetic material from the time-dependent spin density functional theory in the linear response regime. The equation of motion for the magnetization includes, besides the static spin stiffness, a "Berry curvature" correction and a damping term. A gradient expansion scheme based on the homogeneous spin-polarized electron gas is proposed for the latter two quantities, and the first few coefficients of the expansion are calculated to second order in the Coulomb interaction.Comment: 8 pages, no figure

Dynamical exchange-correlation potentials for the electron liquid in the spin channel

URL:http://link.aps.org/doi/10.1103/PhysRevB.68.195113 DOI:10.1103/PhysRevB.68.195113The components of the exchange-correlation kernel tensor of an isotropic electron liquid in the spin channel have the structure f xc,2 L,T (q,v) ! q!0 A(v)/q21BL,T(v), where L denotes the longitudinal component and T the transverse component relative to the direction of the wave vector q. In this paper we calculate analytically the high- and low-frequency limits of A(v) and BL,T(v) and combine these limiting forms with the Kramers-Kro¨nig dispersion relations to obtain approximations for A(v) and BL,T(v) at all frequencies.We gratefully acknowledge support for this work from the NSF Grant No. DMR-0074959 and from the Research Board Grant No. URB-00-029 at the University of Missouri

Dynamical exchange-correlation potentials for an electron liquid

URL:http://link.aps.org/doi/10.1103/PhysRevB.65.235121 DOI:10.1103/PhysRevB.65.235121The imaginary parts of the exchange-correlation kernels fxcL,T(ω) in the longitudinal and transverse current-current response functions of a homogeneous electron liquid are calculated exactly at low frequency, to leading order in the Coulomb interaction. Combining these new results with the previously known high-frequency behaviors of ImfxcL,T(ω) and with the compressibility and the third moment sum rules, we construct simple interpolation formulas for ImfxcL,T(ω) in three and two spatial dimensions. A feature of our interpolation formulas is that they explicitly take into account the two-plasmon component of the excitation spectrum: our longitudinal spectrum ImfxcL(ω) is thus intermediate between the Gross-Kohn interpolation, which ignores the two-plasmon contribution, and a recent approximate calculation by Nifosì, Conti, and Tosi, which probably overestimates it. Numerical results for both the real and imaginary parts of the exchange-correlation kernels at typical electron densities are presented, and compared with those obtained from previous approximations. We also find an exact relation between ImfxcL(ω) and ImfxcT(ω) at small ω.We gratefully acknowledge support for this work from the NSF Grant No. DMR-0074959 and from the Research Board Grant No. URB-00-029 at the University of Missouri

Erratum: Dynamical exchange-correlation potentials for an electron liquid [Phys. Rev. B 65, 235121 (2002)]

URL:http://link.aps.org/doi/10.1103/PhysRevB.71.169904 DOI:10.1103/PhysRevB.71.169904 Erratum concerning http://hdl.handle.net/10355/7762Erratum concerning Dynamical exchange-correlation potentials for an electron liquid [Phys. Rev. B 65, 235121 (2002)

Lifetime of a quasiparticle in an electron liquid

URL:http://link.aps.org/doi/10.1103/PhysRevB.71.075112 DOI:10.1103/PhysRevB.71.075112We calculate the inelastic lifetime of an electron quasiparticle due to Coulomb interactions in an electron liquid at low (or zero) temperature in two and three spatial dimensions. The contribution of “exchange” processes is calculated analytically and is shown to be non-negligible even in the high-density limit in two dimensions. Exchange effects must therefore be taken into account in a quantitative comparison between theory and experiment. The derivation in the two-dimensional case is presented in detail in order to clarify the origin of the disagreements that exist among the results of previous calculations, even the ones that only took into account “direct” processes.We gratefully acknowledge support by NSF Grant Nos. DMR-0074959 and DMR-0313681