Studies relying on hydrodynamic theory and Kardar-Parisi-Zhang (KPZ) scaling have found that in the one-dimensional Hubbard model spin and charge transport are for all temperatures $T>0$ anomalous superdiffusive at zero magnetic field, $h=0$, and zero chemical potential, $\mu =0$, respectively. However, this contradicts recent exact results that at very low temperature charge transport rather is normal diffusive. In this Letter we identify the mechanisms that control the different types of temperature dependence of the $h=0$ spin and $\mu =0$ charge transport and find that the latter is normal diffusive for all finite temperatures $T>0$, in contrast to the hydrodynamic theory and KPZ scaling predictions.

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• Charge
• Charge dynamics
• Electrical conductivity
• Electrical properties
• Magnetic interactions
• Magnetism
• Spin dynamics