the noninteracting band structure: The three-site unit cell gives rise to three energy bands, the middle of which is flat (dispersionless), as is also the case for the Lieb lattice. However, unlike the Lieb lattice for which the flat band touches the dispersing bands above and below it, here the middle band is disconnected from the lower and upper bands for any positive value of $f$-$d$ hybridization $V$. The system is a band insulator at one-third and two-thirds filling. Nevertheless, at half-filling, our focus here, it is similar to the Lieb case, with a partially filled flat band which, as we shall see, gives way to bulk ferromagnetism when interactions are turned on [@Vollhardt01].

![(Color online) Spin-spin correlation functions for nearest pair of sites in the $x$-(or $y$-) direction: (a) $c^{d_{1}d_{1}}(1)$, $c^{d_{0}d_{0}}(1)$, $c^{ff}(1)$, (b) $c^{d_{0}d_{1}}(0.5)$, $c^{d_{1}f}(1)$ and $c^{d_{0}f}(0.5)$. Only correlations between pairs of sites on different sublattices, that is $d_{0}d_{1}$ and $d_{1}f$, are negative (AF).[]{data-label="Fig:Corr_NN"}](correl_NN.pdf)

We fix $U_{f}/t=4$ and vary the strength of the $f$-$d$ hybridization $V/t$. Figure \[Fig:local\_mom\] shows the local moments, $\langle
(\hat{m}^{z}_{\mathbf{i}})^{2} \rangle = \langle (\hat{n}_{\mathbf{i}
\uparrow} - \hat{n}_{\mathbf{i} \downarrow})^{2} \rangle $ on the different types of sites. When $V/t \sim 0.8$, inside the AF phase of 