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

TL;DR

This paper investigates how magnetic order persists in the dilute Hubbard model on a Lieb lattice, revealing that electron itinerancy enhances magnetic resilience beyond classical percolation limits and identifying associated transport transitions.

Contribution

It demonstrates that magnetic order in the Lieb lattice persists at higher dilution levels than classical percolation predicts, highlighting the role of electron itinerancy in flat band systems.

Findings

Magnetic order persists up to nearly twice the classical percolation threshold.

Localized `p' states dominate long-range magnetic correlations.

Transport properties indicate an insulator-to-metal transition near the critical dilution.

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.