  Many strongly correlated systems, including high-temperature superconductors
such as the cuprates, 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, first
identifying a percolation transition that occurs in the low-energy sector at
critical hole doping $p_c\sim 0.19$. We then use the critical properties near
this transition to rewrite the Hubbard Hamiltonian in a way that motivates a
large-$N$ model with strange metallic properties. In particular, we show that
this model has the linear-in-$T$ resistivity and power-law optical conductivity
$\sim |\omega|^{-2/3}$ observed in the strange metal regime of cuprates,
suggesting potential relevance for describing this important class of
materials.
