Diagrammatic self-energy approximations and the total particle number

Details Diagrammatic self-energy approximations and the total particle number Diagrammatic self-energy approximations and the total particle number

2001-10-20

arxiv.org/abs/cond-mat/0110435v1

Phys. Rev. B 64, 235106 (2001).

Physics

Condensed Matter

Materials Science

6 pages including 3 figures, RevTeX

Scientific paper

10.1103/PhysRevB.64.235106

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.

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