Self-consistency and the GW-approximation

Sammanfattning: The effects of self-consistency in the GW-approximation are studied. The $GWA$ is known to describe the electronic properties of a wide range of materials very well. However, the calculations made so far have not taken into account the issue of self-consistency, which is implied in the original formulation of the $GWA$. The role of self-consistency is investigated by calculating the electronic self-energy of the homogeneous electron gas, using the $GWA$ with different levels of self-consistency. It is demonstrated that the physical properties produced by a fully self-consistent scheme do not agree well with experiment. The necessity of vertex corrections is pointed out. However, it is shown that the total energies resulting from this scheme, calculated through the Galitskii-Migdal formula, agree very well with existing Monte-Carlo data. Numerical evidence also confirms that the scheme of full self-consistency fulfills the criteria of a so-called conserving approximation. Further, a scheme of partial self-consistency is presented and investigated. The application of this scheme to a real system lies within reach of present day computer capability. It is found that the partial self-consistency gives a reasonable description of most physical properties.