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

Abstract

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 four-fold 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.

9 pages, 10 figures

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Cited by in corpus (9)

• Antiferromagnetism beyond classical percolation threshold in the site-diluted half-filled one-band Hubbard model in three dimensions
• Percolation on Lieb lattices
• Metal-insulator transition in the disordered Hubbard model of the Lieb lattice
• Snakes on Lieb lattice
• Magnetic impurities in a charge-ordered background
• Altermagnetism and its induced higher-order topology on the Lieb lattice
• Finite temperatures and flat bands: the Hubbard model on three-dimensional Lieb lattices
• An intermediate phase induced by dilution in a correlated Dirac Fermi system
• Spin-imbalance induced buried topological edge currents in Mott \& topological insulator heterostructures