Instability of subdiffusive spin dynamics in strongly disordered Hubbard chain

We study spin transport in a Hubbard chain with a strong, random, on-site potential and with spin-dependent hopping integrals t(sigma). For the SU(2) symmetric case t(up arrow) = t(down arrow), such a 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(up arrow) not equal t(down arrow )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(up arrow) not equal t(down arrow). Instability of the spin subdiffusion originates from an interplay between random effective fields and singularly distributed random exchange interactions.