Theory of a strange metal in the doped Hubbard model via percolation

Many strongly correlated systems, including high-temperature superconductors, exhibit strange metallic behavior in certain regimes, characterized by anomalous transport properties that are irreconcilable with a Fermi-liquid-like description in terms of quasiparticles. One standard theoretical starting point to examine the properties of such systems is the Hubbard model, which has also been found to display non-Fermi-liquid behavior in simulations. Here we study the two-dimensional hole-doped Hubbard model employing a basis that highlights a percolation transition in the low-energy sector at critical hole doping p_c ~ 0.19. We demonstrate that near this transition the model can be exactly rewritten to motivate a large-N model that yields strange metallic properties. In particular, we show that this model gives the same power-law optical conductivity observed in the strange metal regime of cuprates, suggesting potential relevance for describing this important class of materials.