Bad metallic transport in a modified Hubbard model

Abstract

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.

arXiv comment13 pages plus supplementary material. 13 figures. v2: improved presentation. v3: improved presentation, thermoelectric conductivity fixed and discussion of localization added

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