1$ (nearest neighbors), (b) $\sqrt{2}$ (next-nearest neighbors) and (c) $4\sqrt{2}$ far from the magnetic defect. As in Figs.\[Fig:local\_DOS\_Nf\_contour\] and \[Fig:local\_DOS\_Nc\_contour\], we fixed $\beta t= 20$. We also present in Fig. \[Fig:local\_DOS\_Nf\](d) the DOS of the undepleted PAM, at the same temperature and hybridization. Notice that for $V/t=1.20$, the undepleted PAM is in the spin-singlet phase and has a gap in the DOS. Although the charge gap of the homogeneous system is recovered at large $|{\bf i}|$, the results suggest that a single depletion in the spin singlet phase of the PAM creates non-vanishing spectral weight in the $f$-sites around the defect (and a localized state in the unpaired $d$ orbital). Similar analyses within a mean-field approach were performed in Refs.  and , where a gain is also observed in spectral weight owing to $f$-orbital depletion.

To summarize: our results provide evidence of enhancement of short range magnetic correlations and local density of states, which we interpret as arising from the breaking of spin singlets near the impurity [@CYu96; @Mendes17]. We now turn to the main theme of this manuscript, namely what happens with a regular collection of depleted sites, and specifically, do the local magnetic regions coalesce into long range 