Momentum Distribution of the Homogeneous Electron Gas

We calculate the off-diagonal density matrix of the homogeneous electron gas at zero temperature using unbiased reptation Monte Carlo calculations for various densities and extrapolate the momentum distribution and the kinetic and potential energies to the thermodynamic limit. Our results on the renormalization factor allow us to validate approximate $G_0{W}_0$ calculations concerning quasiparticle properties over a broad density region ($1\le r_s\lesssim 10$) and show that, near the Fermi surface, vertex corrections and self-consistency aspects almost cancel each other out.

Figure 1

The momentum distribution ($n_k$) of the unpolarized electron gas for various densities extrapolated to the thermodynamic limit. The inset shows the extrapolation of $n_k$ for $r_s=5$ from a system with $N=54$ electrons to the thermodynamic limit, $N\to \infty$, leading to a significant reduction of the renormalization factor $Z$.