Spin-mediated particle transport in the disordered Hubbard model

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