132 research outputs found

### 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

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