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 bad metals, by restoring in the well-known Hubbard model—with hopping $t$ and on-site repulsion $U$—a “screened Coulomb” interaction between charge densities that decays exponentially with spatial separation. This interaction 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 Wiedemann-Franz law and a large thermopower that can undergo sign change.

Figure 1

On-site energies for a typical configuration with a $29\times 29$ lattice at temperature $k_{B}T=0.76U$, coupling $V=0.1U$, range $\ell =2a$, and filling $n=0.63$. (Top left panel) Occupation numbers for the configuration (white is unoccupied, gray is singly occupied, and black is doubly occupied). (Top right panel) On-site potentials for up spins, ${\epsilon }_{i\uparrow }$, generated by this configuration. A broadened upper (red and yellow) and a lower (blue) Hubbard band are seen. (Bottom panel) The corresponding low frequency conductance peak. The solid line shows a fit to a Gaussian. (Inset) The optical conductivity over a wider frequency range, including transitions between the lower and upper Hubbard bands.

Figure 2

Resistivity as a function of temperature. Statistical errors are shown.

Figure 3

Current relaxation rate as a function of temperature. (Inset) Inverse Drude weight as of function of temperature. The statistical uncertainty in the fit to Eq. (3) is negligible.

Figure 4

(Left panel) Violation of the Wiedemann-Franz law across the phase diagram. The Sommerfeld value $L_0\equiv {\pi }^2/3\times (k_B/e{)}^2$. (Right panel) Fraction of the electronic kinetic energy in the conductance peak—as measured by $\mathcal{D}/K_{\mathrm{tot}}$.

Figure 5

Inverse diffusivity against temperature. The larger errors bars on the diffusivity are due to a near cancellation in the computation of $\kappa$ and $c_n$; see the Supplemental Material [14]. (Inset) Inverse susceptibility against temperature.