Instability of subdiffusive spin dynamics in strongly disordered Hubbard chain

We study spin transport in a Hubbard chain with strong, random, on--site potential and with spin--dependent hopping integrals, $t_{\sigma}$. For the the SU(2) symmetric case, $t_{\uparrow} =t_{\downarrow}$, such model exhibits only partial many-body localization with localized charge and (delocalized) subdiffusive spin excitations. Here, we demonstrate that breaking the SU(2) symmetry by even weak spin--asymmetry, $t_{\uparrow} \ne t_{\downarrow}$, localizes spins and restores full many-body localization. To this end we derive an effective spin model, where the spin subdiffusion is shown to be destroyed by arbitrarily weak $t_{\uparrow} \ne t_{\downarrow}$. Instability of the spin subdiffusion originates from an interplay between random effective fields and singularly distributed random exchange interactions.