  We derive and study the effective spin model that explains the anomalous spin
dynamics in the one-dimensional Hubbard model with strong potential disorder.
Assuming that charges are localized, we show that spins are delocalized and
their subdiffusive transport originates from a singular random distribution of
spin exchange interactions. The exponent relevant for the subdiffusion is
determined by the Anderson localization length and the density of electrons.
While the analytical derivations are valid for low particle density, numerical
results for the full model reveal a qualitative agreement up to half-filling.
