109 research outputs found
Decay properties of the one-particle Green function in real space and imaginary time
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.Comment: 4 pages, RevTe
Variational solution of the T-matrix integral equation
We present a variational solution of the T-matrix integral equation within a
local approximation. This solution provides a simple form for the T matrix
similar to Hubbard models but with the local interaction depending on momentum
and frequency. By examining the ladder diagrams for irreducible polarizability,
a connection between this interaction and the local-field factor is
established. Based on the obtained solution, a form for the T-matrix
contribution to the electron self-energy in addition to the GW term is
proposed. In the case of the electron-hole multiple scattering, this form
allows one to avoid double counting.Comment: 7 pages, 7 figure
Diagrammatic self-energy approximations and the total particle number
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 G(0)W(0) 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
Spectra and total energies from self-consistent many-body perturbation theory
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 GW Gamma 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. [S0163-1829 (98)05040-1]
Density-Matrix functional theory of strongly-correlated lattice fermions
A density functional theory (DFT) of lattice fermion models is presented,
which uses the single-particle density matrix gamma_{ij} as basic variable. A
simple, explicit approximation to the interaction-energy functional W[gamma] of
the Hubbard model is derived from exact dimer results, scaling properties of
W[gamma] and known limits. Systematic tests on the one-dimensional chain show a
remarkable agreement with theBethe-Ansatz exact solution for all interaction
regimes and band fillings. New results are obtained for the ground-state
energyand charge-excitation gap in two dimensions. A successful description of
strong electron correlations within DFT is achieved.Comment: 15 pages, 6 figures Submitted to PR
Many-body GW calculations of ground-state properties: Quasi-2D electron systems and van der Waals forces
We present GW many-body results for ground-state properties of two simple but very distinct families of inhomogeneous systems in which traditional implementations of density-functional theory (DFT) fail drastically. The GW approach gives notably better results than the well-known random-phase approximation, at a similar computational cost. These results establish GW as a superior alternative to standard DFT schemes without the expensive numerical effort required by quantum Monte Carlo simulations
Systematic vertex corrections through iterative solution of Hedin's equations beyond the it GW approximation
We present a general procedure for obtaining progressively more accurate functional expressions for the electron self-energy by iterative solution of Hedin's coupled equations. The iterative process starting from Hartree theory, which gives rise to the GW approximation, is continued further, and an explicit formula for the vertex function from the second full cycle is given. Calculated excitation energies for a Hubbard Hamiltonian demonstrate the convergence of the iterative process and provide further strong justification for the GW approximation
The charge density of semiconductors in the GW approximation
We present a method to calculate the electronic charge density of periodic solids in the GW approximation, using the space-time method. We investigate for the examples of silicon and germanium to what extent the GW approximation is charge-conserving and how the charge density compares with experimental values. We find that the GW charge density is close to experiment and charge is practically conserved. We also discuss how using a Hartree potential consistent with the level of approximation affects the quasi-particle energies and find that the common simplification of using the LDA Hartree potential is a very well justified
Exchange-correlation kernels for excited states in solids
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
wavevector 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.Comment: 7 pages including 5 figures, RevTe
Density-matrix functional theory of the Hubbard model: An exact numerical study
A density functional theory for many-body lattice models is considered in
which the single-particle density matrix is the basic variable. Eigenvalue
equations are derived for solving Levy's constrained search of the interaction
energy functional W, which is expressed as the sum of Hartree-Fock energy and
the correlation energy E_C. Exact results are obtained for E_C of the Hubbard
model on various periodic lattices. The functional dependence of E_C is
analyzed by varying the number of sites, band filling and lattice structure.
The infinite one-dimensional chain and one-, two-, or three-dimensional finite
clusters with periodic boundary conditions are considered. The properties of
E_C are discussed in the limits of weak and strong electronic correlations, as
well as in the crossover region. Using an appropriate scaling we observe a
pseudo-universal behavior which suggests that the correlation energy of
extended systems could be obtained quite accurately from finite cluster
calculations. Finally, the behavior of E_C for repulsive (U>0) and attractive
(U<0) interactions are contrasted.Comment: Phys. Rev. B (1999), in pres
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