  We present numerical results within the one-dimensional disordered Hubbard
model for several characteristic indicators of the many-body localization
(MBL). Considering traditionally studied charge disorder (i.e., the same
disorder strength for both spin orientations) we find that even at strong
disorder all signatures consistently show that while charge degree of freedom
is non-ergodic, the spin is delocalized and ergodic. This indicates the absence
of the full MBL in the model that has been simulated in recent cold-atom
experiments. Full localization can be restored if spin-dependent disorder is
used instead.
