Dielectric function and thermodynamic properties of jellium in the GW   approximation
  The fully self-consistent GW approximation is an established method for electronic structure calculations. Its most serious deficiency is known to be an incorrect prediction of the dielectric response. In this work we examine the GW approximation for the homogeneous electron gas and find that problems with the dielectric response are solved by enforcing the particle-number conservation law in the polarization function. Previously reported data for the ground-state energy were plainly contradicting each other well outside of reported error bounds. Some of these results created a false impression of how accurate the fully self-consistent GW approximation is. We resolve this controversy by confirming that only Ref. [15] was reporting correct energy data, and present values for other key Fermi-liquid properties. 
Kris Van Houcke, Igor S. Tupitsyn, Andrey S. Mishchenko, Nikolay V.   Prokof'ev
cond-mat.str-el cond-mat.mtrl-sci