36 research outputs found
Self-consistency and vertex corrections beyond the GW approximation
The good performance of the GW approximation for band-structure calculations
in solids was long taken as a sign that the sum of self-energy diagrams is
converged and that all omitted terms are small. However, with modern
computational resources it has now become possible to evaluate self-consistency
and vertex corrections explicitly, and the numerical results show that they
are, in general, not individually negligible. In this review the available data
is examined, and the implications for practical calculations and the
theoretical foundation of the GW approximation are discussed.Comment: 10 pages including 1 figure, LaTe
Universality of the Hohenberg-Kohn functional
We comment on a recent article by H. L. Neal [Am. J. Phys. 66, 512 (1998)],
in which an analytic expression for the Hohenberg-Kohn functional was derived
for one-dimensional two-particle systems with the harmonic interaction. We
argue that the functional given by Neal is not exact but really constitutes an
approximation in the same spirit as the local-density approximation.Comment: 2 pages, RevTe
Excitons with anisotropic effective mass
We present a simple analytic scheme for calculating the binding energy of excitons in semiconductors that takes full account of the existing anisotropy in the effective mass, as a complement to the qualitative treatment in most textbooks. Results obtained for excitons in gallium nitride form the basis for a discussion of the accuracy of this approach
Density-functional theory and the v-representability problem for model strongly correlated electron systems
Inspired by earlier work on the band-gap problem in insulators, we reexamine
the treatment of strongly correlated Hubbard-type models within
density-functional theory. In contrast to previous studies, the density is
fully parametrized by occupation numbers and overlap of orbitals centered at
neighboring atomic sites, as is the local potential by the hopping matrix. This
corresponds to a good formal agreement between density-functional theory in
real space and second quantization. It is shown that density-functional theory
is formally applicable to such systems and the theoretical framework is
provided. The question of noninteracting v representability is studied
numerically for finite one-dimensional clusters, for which exact results are
available, and qualitatively for infinite systems. This leads to the conclusion
that the electron density corresponding to interacting systems of the type
studied here is in fact not noninteracting v representable because the
Kohn-Sham electrons are unable to reproduce the correlation-induced
localization correctly.Comment: 9 pages including 1 figur
Efficient calculation of the Coulomb matrix and its expansion around k=0 within the FLAPW method
We derive formulas for the Coulomb matrix within the full-potential
linearized augmented-plane-wave (FLAPW) method. The Coulomb matrix is a central
ingredient in implementations of many-body perturbation theory, such as the
Hartree-Fock and GW approximations for the electronic self-energy or the
random-phase approximation for the dielectric function. It is represented in
the mixed product basis, which combines numerical muffin-tin functions and
interstitial plane waves that are here expanded with the Rayleigh formula. The
resulting algorithm is very efficient in terms of both computational cost and
accuracy and is superior to an implementation with the Fourier transform of the
step function. In order to allow an analytic treatment of the divergence at k=0
in reciprocal space, we expand the Coulomb matrix analytically around this
point without resorting to a projection onto plane waves. We then apply a basis
transformation that diagonalizes the Coulomb matrix and confines the divergence
to a single eigenvalue. At the same time, response matrices like the dielectric
function separate into head, wings, and body with the same mathematical
properties as in a plane-wave basis. As an illustration we apply the formulas
to electron-energy-loss spectra for nickel at different k vectors including
k=0. The convergence of the spectra towards the result at k=0 is clearly seen.
Our treatment also allows to include transitions from core states that give
rise to a shallow peak at high energies and lead to good agreement with
experiment.Comment: 18 pages, 3 figure
Optical conductivity of metals from first principles
A computational method to obtain optical conductivities from first principles
is presented. It exploits a relation between the conductivity and the complex
dielectric function, which is constructed from the full electronic band
structure within the random-phase approximation. In contrast to the Drude
model, no empirical parameters are used. As interband transitions as well as
local-field effects are properly included, the calculated spectra are valid
over a wide frequency range. As an illustration I present quantitative results
for selected simple metals, noble metals, and ferromagnetic transition metals.
The implementation is based on the full-potential linearized
augmented-plane-wave method.Comment: 3 pages including 5 figure
Quasiparticle Corrections to the Electronic Properties of Anion Vacancies at GaAs(110) and InP(110)
We propose a new method for calculating optical defect levels and
thermodynamic charge-transition levels of point defects in semiconductors,
which includes quasiparticle corrections to the Kohn-Sham eigenvalues of
density-functional theory. Its applicability is demonstrated for anion
vacancies at the (110) surfaces of III-V semiconductors. We find the (+/0)
charge-transition level to be 0.49 eV above the surface valence-band maximum
for GaAs(110) and 0.82 eV for InP(110). The results show a clear improvement
over the local-density approximation and agree closely with an experimental
analysis.Comment: 4 pages including 1 figure, RevTe
First-principles calculation of electronic excitations in solids with SPEX
We describe the software package SPEX, which allows first-principles
calculations of quasiparticle and collective electronic excitations in solids
using techniques from many-body perturbation theory. The implementation is
based on the full-potential linearized augmented-plane-wave (FLAPW) method,
which treats core and valence electrons on an equal footing and can be applied
to a wide range of materials, including transition metals and rare earths.
After a discussion of essential features that contribute to the high numerical
efficiency of the code, we present illustrative results for quasiparticle band
structures calculated within the GW approximation for the electronic
self-energy, electron-energy-loss spectra with inter- and intraband transitions
as well as local-field effects, and spin-wave spectra of itinerant
ferromagnets. In all cases the inclusion of many-body correlation terms leads
to very good quantitative agreement with experimental spectroscopies.Comment: 12 pages including 6 figure
Assessment of the GW Approximation using Hubbard Chains
We investigate the performance of the GW approximation by comparison to exact results for small model systems. The role of the chemical potentials in Dyson's equation as well as the consequences of numerical resonance broadening are examined, and we show how a proper treatment can improve computational implementations of many-body perturbation theory in general. GW and exchange-only calculations are performed over a wide range of fractional band fillings and correlation strengths. We thus identify the physical situations where these schemes are applicable