is as follows: In Sec. II we define the tight-binding Hamiltonian precisely, review the Determinant Quantum Monte Carlo (DQMC) methodology[@blankenbecler81] briefly, and define the observables used to characterize the model’s properties. Section III presents data on the effect of the removal of a single site; the resulting enhanced spin response provides an initial clue to the robustness of magnetism in the regularly depleted geometry, described in Sec. IV. Section V analyzes data for the compressibility, effective hopping, and conductivity, and Sec. VI contains our conclusions.

Model {#Model and Method}
=====

The depleted PAM we consider here is described by the Hamiltonian $$\begin{aligned}
 \label{eq:PAM_hamil}
\nonumber \hat {\mathcal H} = &
-t \sum_{\langle \mathbf{i}, \mathbf{j} \rangle, \sigma} 
\big(d^{\dagger}_{\mathbf{i} \sigma} d^{\phantom{\dagger}}_{\mathbf{j} \sigma} + {\rm h.c.} \big)
 - V \sideset{}{'}\sum_{ \mathbf{i} \sigma}
\big(d^{\dagger}_{\mathbf{i} \sigma} 
f^{\phantom{\dagger}}_{\mathbf{i} \sigma} + {\rm h.c.} \big) 
\\ \nonumber 
& + U_{f} \sideset{}{'}\sum_{\mathbf{i}}
\big(n^{f}_{\mathbf{i} \uparrow} - \frac{1}{2} \big) 
\big(n^{f}_{\mathbf{i} \downarrow} - \frac{1}{2} \big)
\\ \nonumber 
& + \sum_{\mathbf{i} \sigma} \epsilon^{d}_{\mathbf{i}}
d^{\dagger}_{\mathbf{i} \sigma} d^{\phantom{\dagger}}_{\mathbf{i} \sigma}
+ \sideset{}{'}\sum_{\mathbf{i} \sigma} \epsilon^{f}_{\mathbf{i}} 
f^{\dagger}_{\mathbf{i} \sigma} f^{\phantom{\dagger}}_{\mathbf{i} \sigma}
\\
& -\mu \sum_{\mathbf{i} \sigma}
d^{\dagger}_{\mathbf{i} \sigma} d^{\phantom{\dagger}}_{\mathbf{i} \sigma}
+ \sideset{}{'}\sum_{\mathbf{i} \sigma}
f^{\dagger}_{\mathbf{i} \sigma} f^{\phantom{\dagger}}_{\mathbf{i} \sigma}
,\end{aligned}$$ where the unprimed sums over $\mathbf{i}$ run over a two dimensional square 