Self-consistent Green functions for the Anderson impurity model

White, J. A.

doi:10.1103/physrevb.45.1100

Cited by 45 publications

(49 citation statements)

References 31 publications

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“…We find that the self-consistent 2B and GW approximations always fail to capture these sidebands and instead distribute the spectral weight as a broad slowly decaying tail. 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 Functionsupporting

confidence: 83%

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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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Section: A Equilibrium Spectral Functionsupporting

confidence: 83%

“…The reason is that the RPA response function is ill defined around the nonmagnetic, and thus unstable, G 0 . The problem has been previously mentioned by White 69 and was brought to the authors attention by Spataru.…”

Section: Instability Of the Nonmagnetic Ground Statementioning

confidence: 88%

ConservingGWscheme for nonequilibrium quantum transport in molecular contacts

2008

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“…[64], as was also pointed out by Ref. [63]. We also note that in the single-shot ring approximation, N C increases slightly as increases.…”

Section: Example Of the Generalized Sum Rulesupporting

confidence: 66%

“…Instead, as in Ref. [63], we performed self-consistency with smaller values of U , and then starting new calculations with this initial guess.…”

Section: Analytical Properties In the Anderson Modelmentioning

confidence: 99%

Partial self-consistency and analyticity in many-body perturbation theory: Particle number conservation and a generalized sum rule

Karlsson

Leeuwen

2016

Phys. Rev. B

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We consider a general class of approximations which guarantees the conservation of particle number in many-body perturbation theory. To do this we extend the concept of Φ-derivability for the self-energy Σ to a larger class of diagrammatic terms in which only some of the Green's function lines contain the fully dressed Green's function G. We call the corresponding approximations for Σ partially Φ-derivable. A special subclass of such approximations, which are gauge-invariant, is obtained by dressing loops in the diagrammatic expansion of Φ consistently with G. These approximations are number conserving but do not have to fulfill other conservation laws, such as the conservation of energy and momentum. From our formalism we can easily deduce if commonly used approximations will fulfill the continuity equation, which implies particle number conservation. We further show how the concept of partial Φ-derivability plays an important role in the derivation of a generalized sum rule for the particle number, which reduces to the Luttinger-Ward theorem in the case of a homogeneous electron gas, and the Friedel sum rule in the case of the Anderson model. To do this we need to ensure that the Green's function has certain complex analytic properties, which can be guaranteed if the spectral function is positive semi-definite. The latter property can be ensured for a subset of partially Φ-derivable approximations for the self-energy, namely those that can be constructed from squares of so-called half-diagrams. In case the analytic requirements are not fulfilled we highlight a number of subtle issues related to branch cuts, pole structure and multivaluedness. We also show that various schemes of computing the particle number are consistent for particle number conserving approximations.

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“…However, as we show in a consecutive paper, 47 the problem of the width of the Kondo resonance as well as that of current conservation can be overcome at the expense of getting somewhat poorer resolution of the Hubbard peaks by using the method of fluctuation exchange approximation. 47,60…”

Section: Discussionmentioning

confidence: 99%

Nonequilibrium transport theory of the singlet-triplet transition: Perturbative approach

2010

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We use a simple iterative perturbation theory to study the singlet-triplet (ST) transition in lateral and vertical quantum dots, modeled by the non-equilibrium two-level Anderson model. To a great surprise, the region of stable perturbation theory extends to relatively strong interactions, and this simple approach is able to reproduce all experimentally-observed features of the ST transition, including the formation of a dip in the differential conductance of a lateral dot indicative of the two-stage Kondo effect, or the maximum in the linear conductance around the transition point. Choosing the right starting point to the perturbation theory is, however, crucial to obtain reliable and meaningful results.

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Self-consistent Green functions for the Anderson impurity model

Cited by 45 publications

References 31 publications

ConservingGWscheme for nonequilibrium quantum transport in molecular contacts

ConservingGWscheme for nonequilibrium quantum transport in molecular contacts

Partial self-consistency and analyticity in many-body perturbation theory: Particle number conservation and a generalized sum rule

Nonequilibrium transport theory of the singlet-triplet transition: Perturbative approach

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