Strange diffusivity and incoherent transport on approach to an antiferromagnetic insulator

We study charge transport across the metal-insulator crossover of the half-filled two-dimensional Hubbard model with controlled accuracy. The dynamical current-current correlation function is evaluated directly in the thermodynamic limit, and the optical conductivity is obtained by numerical analytic continuation. Our multiscale scheme combines unbiased diagrammatic Monte Carlo at low frequencies with a self-consistent semi-analytic diagrammatic treatment at high frequencies. Over a broad temperature range where the DC resistivity follows anomalous scaling,∼T^α with 0 < α ≲ 1, the simple Nernst-Einstein relation yields the diffusivity with the characteristic∼1/sqrt(T) “strange metal” behavior. It was also revealed that the insulating regime is entered through a peculiar non-Fermi liquid state—which we call a Pseudogap Metal —characterized by insulating charge compressibility coexisting with metallic transport while the one-particle self energy captures a significant anisotropy. Diagrammatically, we shows that the high-temperature incoherent transport is captured by the dressed polarization bubble, whereas near the metal-insulator crossover, the effective interaction vertex between opposite-spin particles is responsible for transferring the Drude weight to a high-frequency continuum.