Many-Body $\mathit{GW}$ Calculations of Ground-State Properties: Quasi-2D Electron Systems and van der Waals Forces

We present $\mathrm{GW}$ many-body results for ground-state properties of two simple but very distinct families of inhomogeneous systems in which traditional implementations of density-functional theory (DFT) fail drastically. The $\mathrm{GW}$ approach gives notably better results than the well-known random-phase approximation, at a similar computational cost. These results establish $\mathrm{GW}$ as a superior alternative to standard DFT schemes without the expensive numerical effort required by quantum Monte Carlo simulations.