Bad metallic transport in a modified Hubbard model

Strongly correlated metals often display anomalous transport, including $T$-linear resistivity above the Mott-Ioffe-Regel limit. We introduce a tractable microscopic model for such bad metals, by supplementing the well-known Hubbard model --- with hopping $t$ and on-site repulsion $U$ --- with a `screened Coulomb' interaction between charge densities that decays exponentially with spatial separation. This interaction entirely lifts the extensive degeneracy in the spectrum of the $t=0$ Hubbard model, allowing us to fully characterize the small $t$ electric, thermal and thermoelectric transport in our strongly correlated model. Throughout the phase diagram we observe $T$-linear resistivity above the Mott-Ioffe-Regel limit, together with strong violation of the Weidemann-Franz law and a large thermopower that can undergo sign change. At intermediate temperatures $t \ll k_B T \lesssim U$, the approximate $T$-linear resistivity arises from a cancellation between the nontrivial temperature dependence of both diffusivities and thermodynamic susceptibilities, as observed in recent transport experiments on cold atomic gases.