Dynamical resilience to disorder: The dilute Hubbard model on the Lieb lattice

In itinerant systems, electron-electron interactions may lead to the formation of local magnetic moments and their effective exchange coupling, which in turn gives rise to long-range magnetic order. Therefore, when moment formation is weakened, such as in the single-band Hubbard model on a square lattice with the on-site repulsion being randomly switched off on a fraction $x$ of sites, magnetic order is suppressed beyond some critical ${x}_c$, which was found to lie below the classical percolation threshold ${x}_c^{\text{(perc,sq)}}$. Here we study dilute magnetism in flat band systems, namely, in the Hubbard model on a ``Lieb'' lattice. Interestingly, we show that magnetic order persists to $x$ almost twice as large as the classical percolation threshold for the lattice, thus emphasizing the central role of electron itinerancy to the magnetic response. The analysis of the orbital-resolved order parameters reveals that the contribution of the fourfold coordinated ``$d$'' sites to magnetism is dramatically affected by dilution, while the localized ``$p$'' states of the flat band provide the dominant contribution to long-range correlations. We also examine the transport properties, which suggest the existence of an insulator-to-metal transition in the same range of the critical magnetic dilution.