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Diagrammatic expansion for positive spectral functions beyond GW: Application to vertex corrections in the electron gas
- Source :
- Phys. Rev. B 90, 115134 (2014)
- Publication Year :
- 2014
-
Abstract
- We present a diagrammatic approach to construct self-energy approximations within many-body perturbation theory with positive spectral properties. The method cures the problem of negative spectral functions which arises from a straightforward inclusion of vertex diagrams beyond the GW approximation. Our approach consists of a two-steps procedure: we first express the approximate many-body self-energy as a product of half-diagrams and then identify the minimal number of half-diagrams to add in order to form a perfect square. The resulting self-energy is an unconventional sum of self-energy diagrams in which the internal lines of half a diagram are time-ordered Green's functions whereas those of the other half are anti-time-ordered Green's functions, and the lines joining the two halves are either lesser or greater Green's functions. The theory is developed using noninteracting Green's functions and subsequently extended to self-consistent Green's functions. Issues related to the conserving properties of diagrammatic approximations with positive spectral functions are also addressed. As a major application of the formalism we derive the minimal set of additional diagrams to make positive the spectral function of the GW approximation with lowest-order vertex corrections and screened interactions. The method is then applied to vertex corrections in the three-dimensional homogeneous electron gas by using a combination of analytical frequency integrations and numerical Monte-Carlo momentum integrations to evaluate the diagrams.<br />Comment: 19 pages, 19 figures
- Subjects :
- Condensed Matter - Other Condensed Matter
Subjects
Details
- Database :
- arXiv
- Journal :
- Phys. Rev. B 90, 115134 (2014)
- Publication Type :
- Report
- Accession number :
- edsarx.1408.6163
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevB.90.115134