TY - JOUR
AB - The performance of several common approximations for the exchange-correlation kernel within time-dependent density-functional theory is tested for elementary excitations in the homogeneous electron gas. Although the adiabatic local-density approximation gives a reasonably good account of the plasmon dispersion, systematic errors are pointed out and traced to the neglect of the wave-vector dependence. Kernels optimized for atoms are found to perform poorly in extended systems due to an incorrect behavior in the long-wavelength limit, leading to quantitative deviations that significantly exceed the experimental error bars for the plasmon dispersion in the alkali metals.
AU - Tatarczyk, Krzysztof
AU - Schindlmayr, Arno
AU - Scheffler, Matthias
ID - 18615
IS - 23
JF - Physical Review B
SN - 0163-1829
TI - Exchange-correlation kernels for excited states in solids
VL - 63
ER -
TY - JOUR
AB - There is increasing interest in many-body perturbation theory as a practical tool for the calculation of ground-state properties. As a consequence, unambiguous sum rules such as the conservation of particle number under the influence of the Coulomb interaction have acquired an importance that did not exist for calculations of excited-state properties. In this paper we obtain a rigorous, simple relation whose fulfilment guarantees particle-number conservation in a given diagrammatic self-energy approximation. Hedin’s G0W0 approximation does not satisfy this relation and hence violates the particle-number sum rule. Very precise calculations for the homogeneous electron gas and a model inhomogeneous electron system allow the extent of the nonconservation to be estimated.
AU - Schindlmayr, Arno
AU - García-González, Pablo
AU - Godby, Rex William
ID - 18612
IS - 23
JF - Physical Review B
SN - 0163-1829
TI - Diagrammatic self-energy approximations and the total particle number
VL - 64
ER -
TY - JOUR
AB - The decay properties of the one-particle Green function in real space and imaginary time are systematically studied for solids. I present an analytic solution for the homogeneous electron gas at finite and at zero temperature as well as asymptotic formulas for real metals and insulators that allow an analytic treatment in electronic-structure calculations based on a space-time representation. The generic dependence of the decay constants on known system parameters is used to compare the scaling of reciprocal-space algorithms for the GW approximation and the space-time method.
AU - Schindlmayr, Arno
ID - 18617
IS - 19
JF - Physical Review B
SN - 0163-1829
TI - Decay properties of the one-particle Green function in real space and imaginary time
VL - 62
ER -
TY - JOUR
AB - With the aim of identifying universal trends, we compare fully self-consistent electronic spectra and total energies obtained from the GW approximation with those from an extended GWΓ scheme that includes a nontrivial vertex function and the fundamentally distinct Bethe-Goldstone approach based on the T matrix. The self-consistent Green’s function G, as derived from Dyson’s equation, is used not only in the self-energy but also to construct the screened interaction W for a model system. For all approximations we observe a similar deterioration of the spectrum, which is not removed by vertex corrections. In particular, satellite peaks are systematically broadened and move closer to the chemical potential. The corresponding total energies are universally raised, independent of the system parameters. Our results, therefore, suggest that any improvement in total energy due to self-consistency, such as for the electron gas in the GW approximation, may be fortuitous.
AU - Schindlmayr, Arno
AU - Pollehn, Thomas Joachim
AU - Godby, Rex William
ID - 18620
IS - 19
JF - Physical Review B
SN - 0163-1829
TI - Spectra and total energies from self-consistent many-body perturbation theory
VL - 58
ER -
TY - JOUR
AB - We present a nontrivial model system of interacting electrons that can be solved analytically in the GW approximation. We obtain the particle number from the GW Green’s function strictly analytically, and prove that there is a genuine violation of particle number conservation if the self-energy is calculated non-self-consistently from a zeroth order Green’s function, as done in virtually all practical implementations. We also show that a simple shift of the self-energy that partially restores self-consistency reduces the numerical deviation significantly.
AU - Schindlmayr, Arno
ID - 18628
IS - 7
JF - Physical Review B
SN - 0163-1829
TI - Violation of particle number conservation in the GW approximation
VL - 56
ER -
TY - JOUR
AB - 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-dimnsional 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.
AU - Schindlmayr, Arno
AU - Godby, Rex William
ID - 18630
IS - 16
JF - Physical Review B
SN - 0163-1829
TI - Density-functional theory and the v-representability problem for model strongly correlated electron systems
VL - 51
ER -