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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., Comment: 9 pages, 10 figures

The Kondo and Periodic Anderson Model (PAM) are known to provide a microscopic picture of many of the fundamental properties of heavy fermion materials and, more generally, a variety of strong correlation phenomena in $4f$ and $5f$ systems. In this paper, we apply the Determinant Quantum Monte Carlo (DQMC) method to include disorder in the PAM, specifically the removal of a fraction $x$ of the localized orbitals. We determine the evolution of the coherence temperature $T^*$, where the local moments and conduction electrons become entwined in a heavy fermion fluid, with $x$ and with the hybridization $V$ between localized and conduction orbitals. We recover several of the principal observed trends in $T^*$ of doped heavy fermions, and also show that, within this theoretical framework, the calculated Nuclear Magnetic Resonance (NMR) relaxation rate tracks the experimentally measured behavior in pure and doped CeCoIn$_5$. Our results contribute to important issues in the interpretation of local probes of disordered, strongly correlated systems., Comment: 8 pages, 4 figures

Light propagation through 1D disordered structures composed of alternating layers, with random thicknesses, of air and a dispersive metamaterial is theoretically investigated. Both normal and oblique incidences are considered. By means of numerical simulations and an analytical theory, we have established that Anderson localization of light may be suppressed: (i) in the long wavelength limit, for a finite angle of incidence which depends on the parameters of the dispersive metamaterial; (ii) for isolated frequencies and for specific angles of incidence, corresponding to Brewster anomalies in both positive- and negative-refraction regimes of the dispersive metamaterial. These results suggest that Anderson localization of light could be explored to control and tune light propagation in disordered metamaterials., Comment: 4 two-column pages, 3 figures

We study the effect of random dilution of attraction centers on electron pairing in a generalization of the negative $U$ Hubbard model where the interaction $U_i$, defined on the two dimensional lattice, can be $-|U|$ and 0 with probability $c$ and $1-c$ depending on the lattice site $i$. Using the determinant quantum Monte Carlo approach, we find the critical concentration $c_0$ of negative centers which leads to superconductivity, and show how the evolution of the local density on the two types of sites lends insight into the formation of global phase coherence., Comment: 10 pages, 3 figures, (submitted toPhysica C)