The use of hydrodynamic transport theory seems to indicate that the charge diffusion constant $D$ of the one-dimensional (1D) half-filled Hubbard model, whose Drude weight vanishes, diverges for temperature $T>0$, which would imply anomalous superdiffusive charge transport. Here the leading term of that constant is derived for low finite temperatures $k_{B}T/{\mathrm{\Delta }}_{\eta }\ll 1$ where ${\mathrm{\Delta }}_{\eta }$ is the Mott-Hubbard gap. It only diverges in the $T\to 0$ limit, being finite and decreasing upon increasing $T$ within the $k_{B}T/{\mathrm{\Delta }}_{\eta }\ll 1$ regime. Our exact results both provide valuable physical information on a complex quantum problem and bring about the interesting unsolved issue of how charge transport evolves from normal diffusive for $k_{B}T/{\mathrm{\Delta }}_{\eta }\ll 1$ to anomalous superdiffusive in the $k_{B}T\to \infty$ limit.

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• Charge
• Charge dynamics
• Electrical conductivity
• Hubbard model
• Hydrodynamics