Fully self-consistent<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>GW</mml:mi></mml:math>self-energy of the electron gas

Holm, B.; Barth, Ulf von

doi:10.1103/physrevb.57.2108

Cited by 353 publications

(380 citation statements)

References 13 publications

(10 reference statements)

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“…Comparing Eqs. (3) and (8), one can still find a correspondence between the unperturbed energies of particle orbitals and the excitation spectrum {n} of the system with A + 1 nucleons and between the hole energies and the spectrum {k} of A − 1 nucleons. However, a larger number of states can appear in the correlated systems due to the mixing of sp excitations with more complicated configurations.…”

Section: Formal Development 21 Single-particle Green's Functionmentioning

confidence: 98%

“…While the propagator or Green's function method was the most important tool in the formal development of many-body theory [2] - [6], only in the last ten years has it been applied to many-body problems beyond its meanfield implementation (the Hartree-Fock approximation). Examples of such applications have appeared in atomic [7] and condensed matter physics [8]. In the atomic case, the essential new development involves taking the self-consistent determination of the electron propagator from the Hartree-Fock level to the fully self-consistent inclusion of the second-order self-energy.…”

Section: Introductionmentioning

confidence: 99%

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Self-consistent Green's function method for nuclei and nuclear matter

Dickhoff

Barbieri

2004

Progress in Particle and Nuclear Physics

494

599

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Recent results obtained by applying the method of self-consistent Green's functions to nuclei and nuclear matter are reviewed. Particular attention is given to the description of experimental data obtained from the (e,e ′ p) and (e,e ′ 2N) reactions that determine one and two-nucleon removal probabilities in nuclei since the corresponding amplitudes are directly related to the imaginary parts of the single-particle and two-particle propagators. For this reason and the fact that these amplitudes can now be calculated with the inclusion of all the relevant physical processes, it is useful to explore the efficacy of the method of self-consistent Green's functions in describing these experimental data. Results for both finite nuclei and nuclear matter are discussed with particular emphasis on clarifying the role of short-range correlations in determining various experimental quantities. The important role of long-range correlations in determining the structure of lowenergy correlations is also documented. For a complete understanding of nuclear phenomena it is therefore essential to include both types of physical correlations. We demonstrate that recent experimental results for these reactions combined with the reported theoretical calculations yield a very clear understanding of the properties of all protons in the nucleus. We propose that this knowledge of the properties of constituent fermions in a correlated many-body system is a unique feature of nuclear physics.

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Section: Formal Development 21 Single-particle Green's Functionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Self-consistent Green's function method for nuclei and nuclear matter

Dickhoff

Barbieri

2004

Progress in Particle and Nuclear Physics

494

599

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“…These findings agree well with previous results obtained with the fluctuation-exchange approximation 69 and with GW studies of the homogeneous electron gas, which showed that self-consistency in the GW self-energy washed out the satellite structure in the spectrum. 70 …”

Section: A Equilibrium Spectral Functionmentioning

confidence: 99%

ConservingGWscheme for nonequilibrium quantum transport in molecular contacts

2008

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We give a detailed presentation of our recent scheme to include correlation effects in molecular transport calculations using the nonequilibrium Keldysh formalism. The scheme is general and can be used with any quasiparticle self-energy, but for practical reasons, we mainly specialize to the so-called GW self-energy, widely used to describe the quasiparticle band structures and spectroscopic properties of extended and lowdimensional systems. We restrict the GW self-energy to a finite, central region containing the molecule, and we describe the leads by density functional theory ͑DFT͒. A minimal basis of maximally localized Wannier functions is applied both in the central GW region and the leads. The importance of using a conserving, i.e., fully self-consistent, GW self-energy is demonstrated both analytically and numerically. We introduce an effective spin-dependent interaction which automatically reduces self-interaction errors to all orders in the interaction. The scheme is applied to the Anderson model in and out of equilibrium. In equilibrium at zero temperature, we find that GW describes the Kondo resonance fairly well for intermediate interaction strengths. Out of equilibrium, we demonstrate that the one-shot G 0 W 0 approximation can produce severe errors, in particular, at high bias. Finally, we consider a benzene molecule between featureless leads. It is found that the molecule's highest occupied molecular orbital-lowest unoccupied molecular orbital gap as calculated in GW is significantly reduced as the coupling to the leads is increased, reflecting the more efficient screening in the strongly coupled junction. For the I-V characteristics of the junction, we find that Hartree-Fock ͑HF͒ and G 0 W 0 ͓G HF ͔ yield results closer to GW than does DFT and G 0 W 0 ͓G DFT ͔. This is explained in terms of selfinteraction effects and lifetime reduction due to electron-electron interactions.

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“…Therefore, model systems that permit numerically exact or, ideally, analytic solutions play an important role for developing and testing approximation schemes within many-body perturbation theory, but even the homogeneous electron gas, a frequently employed model in solid-state physics, can only be treated numerically in the GW approximation. Furthermore, with no experimental measurements or independent theoretical benchmark results, even the basic question whether the true occupied band width in the range of metallic densities is smaller than that of free electrons, as predicted by the standard non-self-consistent GW approximation, 5,39 or larger, as obtained when full self-consistency is included, 7,8 is not yet finally settled. Calculations that go beyond the GW approximation and attempt to incorporate the combined effects of self-consistency and vertex corrections remain inconclusive, because the results depend on the choice of vertex function and details of the implementation.…”

Section: Introductionmentioning

confidence: 99%

“…One long-standing controversy centers on the question whether the Green function used to construct the self-energy should be evaluated selfconsistently or not. [7][8][9][10][11][12][13][14][15][16][17] Both approaches can be justified:…”

Section: Introductionmentioning

confidence: 99%

Analytic evaluation of the electronic self-energy in theGWapproximation for two electrons on a sphere

Schindlmayr

2013

Phys. Rev. B

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The GW approximation for the electronic self-energy is an important tool for the quantitative prediction of excited states in solids, but its mathematical exploration is hampered by the fact that it must, in general, be evaluated numerically even for very simple systems. In this paper I describe a nontrivial model consisting of two electrons on the surface of a sphere, interacting with the normal long-range Coulomb potential, and show that the GW self-energy, in the absence of self-consistency, can in fact be derived completely analytically in this case. The resulting expression is subsequently used to analyze the convergence of the energy gap between the highest occupied and the lowest unoccupied quasiparticle orbital with respect to the total number of states included in the spectral summations. The asymptotic formula for the truncation error obtained in this way, whose dominant contribution is proportional to the cutoff energy to the power −3/2, may be adapted to extrapolate energy gaps in other systems.

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Fully self-consistentGWself-energy of the electron gas

Cited by 353 publications

References 13 publications

Self-consistent Green's function method for nuclei and nuclear matter

Self-consistent Green's function method for nuclei and nuclear matter

ConservingGWscheme for nonequilibrium quantum transport in molecular contacts

Analytic evaluation of the electronic self-energy in theGWapproximation for two electrons on a sphere

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