Temperature dependence of charge transport in the half-filled one-dimensional Hubbard model

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 ${k}_{B}T/{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\eta}}\ensuremath{\ll}1$ where ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\eta}}$ is the Mott-Hubbard gap. It only diverges in the $T\ensuremath{\rightarrow}0$ limit, being finite and decreasing upon increasing $T$ within the ${k}_{B}T/{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\eta}}\ensuremath{\ll}1$ 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 ${k}_{B}T/{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\eta}}\ensuremath{\ll}1$ to anomalous superdiffusive in the ${k}_{B}T\ensuremath{\rightarrow}\ensuremath{\infty}$ limit.