Strange metal in the doped Hubbard model via percolation

Many strongly correlated systems exhibit strange metallic behavior in certain parameter regimes characterized by anomalous transport properties that are irreconcilable with a Fermi-liquid-like description in terms of quasiparticles. The Hubbard model is a standard theoretical starting point to examine the properties of such systems and also exhibits non-Fermi-liquid behavior in simulations. Here we analytically study the two-dimensional hole-doped Hubbard model in the large $U$ limit, first identifying a doping-induced percolation transition in the low-energy sector occurring at a definite critical doping $p_c$ depending on lattice structure. Using the critical properties near this transition we rewrite the Hubbard Hamiltonian and motivate a low-energy lattice-independent large-$N$ model with distinct non-Fermi-liquid properties. We show that this model has linear-in-$T$ resistivity with doping-dependent slope maximized at $p=p_c$ and power-law optical conductivity $\sim |\omega|^{-2/3}$. Though the parameters used in developing this theory mean it cannot be directly applied to the cuprate superconductors, we nevertheless reproduce several important phenomena observed in their strange metal phase, and also predict these same qualitative behaviors to manifest in other lattices near concrete hole dopings.