lattice, with $\langle \mathbf{i}, \mathbf{j} \rangle$ denoting nearest-neighbors, while the primed sums are restricted to the set of sites having $f$-orbitals. The specific depletion patterns will be described in the coming sections. The first term on the right-hand side of Eq. represents the hopping of $d$-electrons, while the second term contains the hybridization, $V$, between $d$ and $f$-orbitals. The Coulomb repulsion on localized $f$-orbitals is included in the third term, with $n^{f}_{\mathbf{i} \sigma} =
f^{\dagger}_{\mathbf{i} \sigma} f^{\phantom{\dagger}}_{\mathbf{i} \sigma}$ being the number operator of $f$-electrons. The last two terms correspond to onsite energies $\epsilon^{d}_{\mathbf{i}}$ and $\epsilon^{f}_{\mathbf{i}}$ of $d$ and $f$-orbitals, respectively. The hopping integral $t\equiv 1$ defines the scale of energy.

We analyze Eq. using DQMC, a numerically exact technique in which all sources of error, statistical (from finite sampling times) and systematic (from the discretization of the inverse temperature $\beta$) can be removed to the desired degree of accuracy. The basic idea of the method is the use of the Trotter-Suzuki decomposition to separate the exponentials of the one-body and two-body pieces, $\hat {\mathcal K}$ and $\hat {\mathcal P}$ respectively, in the partition function, ${\cal Z} = {\rm Tr}\, e^{-\beta \hat {\mathcal H} }
= {\rm Tr}\, \big[ \big(
e^{-\Delta\tau 