 ![ \[fig:verification:w0.00-u0.00:ddcorr-frg\]\[f00\] Left column: The density-density correlator as defined in Eq.  calculated at $\Lambda_{\text{c}}$ at $U{=}W{=}0.00$ (upper row, system in Fig. \[f0\]) and at $U{=}W{=}0$ (lower row). The peak indicates the CDW instability with wave-vector $({\mathbf{Q}}{=}\pi,\pi)$. Right column: Respective densities $n({\mathbf{r}})$ from exact diagonalization (ED) exhibiting the correspondig pinned CDW.](figure00