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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 basedon the generalized hydrodynamics theory for a partitioning protocol and showedthe presence of a clogging phenomenon. Clogging is a phenomenon that vanishingcharge current coexists with nonzero energy current, and was found when theprotocol uses the initial condition that the left half of the system isprepared to be half filling at high temperatures with the right half beingempty. Clogging occurs at all the sites in the left half and lasts for a timeproportional to its distance from the connection point. In this paper, we usevarious different initial conditions and discuss two issues. The first issue isthe possibility of clogging in a stationary state. When the electron density inthe right half is initially set nonzero, we found that the left half-filledpart expands for various sets of parameters in the initial condition. Thismeans that the clogging phenomenon occurs at all the sites in the long-timestationary state, and we also discuss its origin. In addition, stationaryclogging is accompanied by a back current, namely, particle density currentflows towards the high-density region. We also found spin clogging occurs forsome initial conditions, i.e., the vanishing spin current coexists with nonzeroenergy current. The second issue is the proportionality of spin and chargecurrents. We have found two spatio-temporal regions where the current ratio isfixed to a nonzero constant. We numerically studied how the current ratiodepends on various initial conditions. We also studied the ratio of charge andenergy currents.

Generalized hydrodynamics study of the one-dimensional Hubbard model: Stationary clogging and proportionality of spin, charge, and energy currents