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Authors: J.A. Berger, L. Reining, and F. Sottile
Affiliations: LSI, Ecole Polytechnique/ CNRS/CEA-DSM, 91128 Palaiseau, France.
European Theoretical Spectroscopy Facility (ETSF).
The GW approximation (GWA) to the self-energy[1] has proved to be very successful in the calculation of quasi-particle energies for a wide range of solids. However, the GWA is computationally expensive which is mainly due to the slow convergence with the number of unoccupied states that have to be taken into account in its standard sum-over-states expression.
In order to overcome this problem one can either use a simplified approximation to the self-energy such as the COHSEX approximation[1] in which no unoccupied states are required, or look for a numerically more efficient approach to the calculation of the GW self-energy such that only a small number of unoccupied states are needed[2]. However, in the former approach one obtains quasi-particle energies that are, in general, not close to the GW energies and in the latter approach one still has to deal with unoccupied states.
In this work we will show that the expression for the GW self-energy can be rewritten in such a way that no unoccupied states enter. This approach leads to a hierarchy of expressions for the self-energy which converges rapidly. We use a similar scheme to rewrite the sum-over-states expression for the polarizability such that only very few unoccupied states are required.
[1] L. Hedin, Phys. Rev. 139, A796 (1965).
[2] F. Bruneval and X. Gonze, Phys. Rev. B 78, 085125 (2008).
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