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Motivated by the recent experiments that reported signatures of many-bodylocalization of ultracold atoms in optical lattices [M. Schreiber {\it et al.},Science {\bf 349}, 842 (2015)], we study dynamics of highly excited states inthe strongly disordered Hubbard model in one dimension. Owing to the $SU(2)$spin symmetry, spin degrees of freedom form a delocalized thermal bath with anarrow bandwidth. The spin bath mediates slow particle transport, eventuallyleading to delocalization of particles. The particle hopping rate isexponentially small in $t/W$ ($t$, $W$ being hopping and disorder scales) owingto the narrow bandwidth of the spin bath. We find the optimal lenghtscale forparticle hopping, and show that the particle transport rate depends strongly onthe density of singly occupied sites in the initial state. The delocalizationrate is zero for initial states with only doubly occupied or empty sites,suggesting that such states are truly many-body localized, and therefore theHubbard model may host both localized and delocalized states. Full many-bodylocalization can be induced by breaking spin rotational symmetry.

Spin-mediated particle transport in the disordered Hubbard model