  In our previous work [Y. Nozawa and H. Tsunetsugu, Phys. Rev. B 101, 035121
(2020)], we studied quench dynamics in the one-dimensional Hubbard model based
on the generalized hydrodynamics theory for a partitioning protocol and showed
the presence of a clogging phenomenon. Clogging is a phenomenon that vanishing
charge current coexists with nonzero energy current, and was found when the
protocol uses the initial condition that the left half of the system is
prepared to be half filling at high temperatures with the right half being
empty. Clogging occurs at all the sites in the left half and lasts for a time
proportional to its distance from the connection point. In this paper, we use
various different initial conditions and discuss two issues. The first issue is
the possibility of clogging in a stationary state. When the electron density in
the right half is initially set nonzero, we found that the left half-filled
part expands for various sets of parameters in the initial condition. This
means that the clogging phenomenon occurs at all the sites in the long-time
stationary state, and we also discuss its origin. In addition, stationary
clogging is accompanied by a back current, namely, particle density current
flows towards the high-density region. We also found spin clogging occurs for
some initial conditions, i.e., the vanishing spin current coexists with nonzero
energy current. The second issue is the proportionality of spin and charge
currents. We have found two spatio-temporal regions where the current ratio is
fixed to a nonzero constant. We numerically studied how the current ratio
depends on various initial conditions. We also studied the ratio of charge and
energy currents.
