Diagrammatic self-energy approximations and the total particle number

A Schindlmayr; P Garcia-Gonzalez; R W Godby

doi:10.1103/PhysRevB.64.235106

Diagrammatic self-energy approximations and the total particle number

A Schindlmayr, P Garcia-Gonzalez, R W Godby

Physics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Article number	235106
Pages (from-to)	-
Number of pages	6
Journal	Physical Review B
Volume	64
Issue number	23
DOIs	https://doi.org/10.1103/PhysRevB.64.235106
Publication status	Published - 15 Dec 2001

Bibliographical note

Keywords

SPACE-TIME METHOD
ELECTRON-GAS
SPECTRAL FUNCTIONS
GW APPROXIMATION
BAND-GAPS
SEMICONDUCTORS
SURFACE
DENSITY
CONSERVATION
INSULATORS

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10.1103/PhysRevB.64.235106

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Cite this

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title = "Diagrammatic self-energy approximations and the total particle number",

abstract = "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.",

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N2 - 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.

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 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.

KW - SPACE-TIME METHOD

KW - ELECTRON-GAS

KW - SPECTRAL FUNCTIONS

KW - GW APPROXIMATION

KW - BAND-GAPS

KW - SEMICONDUCTORS

KW - SURFACE

KW - DENSITY

KW - CONSERVATION

KW - INSULATORS

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