VIOLATION OF PARTICLE NUMBER CONSERVATION IN THE GW APPROXIMATION

We present a nontrivial model system of interacting electrons that can be solved analytically in the GW approximation. We obtain the particl e number from the GW Green's function strictly analytically, and prove that there is a genuine violation of particle number conservation if the self-energy is calculated non-self-consistently from a zeroth orde r Green's function, as done in virtually all practical implementations . We also show that a simple shift of the self-energy that partially r estores self-consistency reduces the numerical deviation significantly .