The spin transport in a strongly interacting spin-pump nanodevice is studied using the time-dependent variational-matrix-product-state approach. The precession magnetic field generates a dissipationless spin current through the quantum dot. We compute the real-time spin current away from the equilibrium condition. Both transient and stationary states are reached in the simulation. The essentially exact results are compared with those from the Hartree-Fock approximation (HFA). It is found that correlation effect on the physical quantities at quasisteady state are captured well by the HFA for small interaction strength. However the HFA misses many features in the real-time dynamics. Results reported here may shed light on the understanding of the ultrafast processes as well as the interplay of the nonequilibrium and strongly correlated effect in the transport properties.
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