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_0W_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.

arXiv comment6 pages including 3 figures, RevTeX

References in corpus (8)

• The GW method
• Self-Consistent Calculation of Total Energies of the Electron Gas Using Many-Body Perturbation Theory
• Enhancements to the GW space-time method
• Jellium surface energy beyond the local-density approximation: Self-consistent-field calculations
• Violation of particle number conservation in the GW approximation
• Efficient Total Energy Calculations from Self-Energy Models
• Decay properties of the one-particle Green function in real space and imaginary time
• The charge density of semiconductors in the GW approximation

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• Combining GW calculations with exact-exchange density-functional theory: An analysis of valence-band photoemission for compound semiconductors
• Ab initio GW electron-electron interaction effects in Quantum Transport
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• Many-body GW Calculations of Ground-State Properties: Quasi-2D Electron Systems and van der Waals Forces
• Momentum distribution and Compton profile by the ab initio GW approximation
• Quasiparticle $GW$ band structures and Fermi surfaces of bulk and monolayer NbS${}_2$
• Hedin's equations and enumeration of Feynman's diagrams
• Analytic evaluation of the electronic self-energy in the GW approximation for two electrons on a sphere
• Partial self-consistency and analyticity in many-body perturbation theory: particle number conservation and a generalized sum rule
• A unified Green's function approach for spectral and thermodynamic properties from algorithmic inversion of dynamical potentials
• Quasiparticle Calculations for Point Defects on Semiconductor Surfaces
• Two-time quantum transport and quantum diffusion
• Condensation energy of the homogeneous electron gas from the density functional theory for superconductors