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Diagrammatic self-energy approximations and the total particle number

Arno Schindlmayr·P. Garcia-Gonzalez·R. W. Godby
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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.

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Arno Schindlmayr, P. Garcia-Gonzalez, R. W. Godby. 2001-10-20. Diagrammatic self-energy approximations and the total particle number. https://doi.org/10.1103/physrevb.64.235106

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