Diagrammatic expansion for positive spectral functions beyond GW: Application to vertex corrections in the electron gas
Abstract
We present a diagrammatic approach to construct selfenergy approximations within manybody 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 twostep procedure: We first express the approximate manybody selfenergy as a product of halfdiagrams and then identify the minimal number of halfdiagrams to add in order to form a perfect square. The resulting selfenergy is an unconventional sum of selfenergy diagrams in which the internal lines of half a diagram are timeordered Green's functions, whereas those of the other half are antitimeordered 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 selfconsistent 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 lowestorder vertex corrections and screened interactions. The method is then applied to vertex corrections in the threedimensional homogeneous electron gas by using a combination of analytical frequency integrations and numerical Monte Carlo momentum integrations to evaluate the diagrams.
 Publication:

Physical Review B
 Pub Date:
 September 2014
 DOI:
 10.1103/PhysRevB.90.115134
 arXiv:
 arXiv:1408.6163
 Bibcode:
 2014PhRvB..90k5134S
 Keywords:

 71.10.w;
 31.15.A;
 73.22.Dj;
 Theories and models of manyelectron systems;
 Ab initio calculations;
 Single particle states;
 Condensed Matter  Other Condensed Matter
 EPrint:
 19 pages, 19 figures