Diagrammatic self-energy approximations and the total particle number

Schindlmayr, Arno; Garcı́a-González, P.; Godby, R. W.

doi:10.1103/physrevb.64.235106

Cited by 33 publications

(32 citation statements)

References 32 publications

(33 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A few attempts to solve this reduced set of equations fully self-consistently have been made in the past. 37,[48][49][50][51][52][53][54][55][56][57][58][59] Although full or partially self-consistent GW calculations can give accurate ground-state total energies and are essential for particle number conservation, 60,61 the quasiparticle properties deteriorate. [49][50][51] This is a result of the successive introduction of higher order electron-electron interaction terms of certain type that are not balanced by other higher order terms contained in the vertex function.…”

Section: ͑4͒mentioning

confidence: 99%

First-principles modeling of localizeddstates with theGW@LDA+Uapproach

et al. 2010

View full text Add to dashboard Cite

First-principles modeling of systems with localized d states is currently a great challenge in condensedmatter physics. Density-functional theory in the standard local-density approximation ͑LDA͒ proves to be problematic. This can be partly overcome by including local Hubbard U corrections ͑LDA+ U͒ but itinerant states are still treated on the LDA level. Many-body perturbation theory in the GW approach offers both a quasiparticle perspective ͑appropriate for itinerant states͒ and an exact treatment of exchange ͑appropriate for localized states͒, and is therefore promising for these systems. LDA+ U has previously been viewed as an approximate GW scheme. We present here a derivation that is simpler and more general, starting from the static Coulomb-hole and screened exchange approximation to the GW self-energy. Following our previous work for f-electron systems ͓H. Jiang, R. I. Gomez-Abal, P. Rinke, and M. Scheffler, Phys. Rev. Lett. 102, 126403 ͑2009͔͒ we conduct a systematic investigation of the GW method based on LDA+ U͑GW @LDA+U͒, as implemented in our recently developed all-electron GW code FHI-gap ͑Green's function with augmented plane waves͒ for a series of prototypical d-electron systems: ͑1͒ ScN with empty d states, ͑2͒ ZnS with semicore d states, and ͑3͒ late transition-metal oxides ͑MnO, FeO, CoO, and NiO͒ with partially occupied d states. We show that for ZnS and ScN, the GW band gaps only weakly depend on U but for the other transition-metal oxides the dependence on U is as strong as in LDA+ U. These different trends can be understood in terms of changes in the hybridization and screening. Our work demonstrates that GW @LDA+U with "physical" values of U provides a balanced and accurate description of both localized and itinerant states.

show abstract

Section: ͑4͒mentioning

confidence: 99%

First-principles modeling of localizeddstates with theGW@LDA+Uapproach

et al. 2010

View full text Add to dashboard Cite

show abstract

“…Furthermore, no mention has been made about how large the violations of the conservation laws are, since this also depends on how strongly correlated the system is [34]. In equilibrium, the violation of particle number seems to be small in some systems [32,33], but larger for other systems [34]; see also Sec. IV C. In biased systems in quantum transport, the violation in the particle current can be as large as the current itself [2,41].…”

Section: Number Conservationmentioning

confidence: 99%

“…Thus, particle conservation is an issue also in equilibrium calculations, a point also stressed in Refs. [32,33].…”

Section: Partial Derivabilitymentioning

confidence: 99%

“…For example, the partially self-consistent GW 0 approximation (where the screened interaction W is kept fixed to be W 0 during the self-consistency cycle) and the non-self-consistent G 0 W 0 approximation are not derivable. However, GW 0 is particle number conserving (first shown for the equilibrium electron gas [26,31], and later more generally [32]) but not fully conserving [33], while G 0 W 0 is not particle number conserving [32,34].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Karlsson

Leeuwen

2016

Phys. Rev. B

View full text Add to dashboard Cite

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.

show abstract

“…42 The analytic solvability was important in this case, because it proved unequivocally that the quantitative deviation was genuine and not due to numerical inaccuracies. A related but even simpler two-site model with a pair of electrons can be treated analytically in the same way.…”

Section: Introductionmentioning

confidence: 99%

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

Schindlmayr

2013

Phys. Rev. B

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Diagrammatic self-energy approximations and the total particle number

Cited by 33 publications

References 32 publications

First-principles modeling of localizeddstates with theGW@LDA+Uapproach

First-principles modeling of localizeddstates with theGW@LDA+Uapproach

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

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

Contact Info

Product

Resources

About