  We introduce time-dependent density matrix renormalization group (tDMRG) as a
solution to long standing problem in spintronics -- how to describe
spin-transfer torque (STT) between flowing spins of conduction electrons and
localized spins within a magnetic material by treating the dynamics of both
spin species fully quantum-mechanically. In contrast to conventional
Slonczewski-Berger STT, where the localized spins are viewed as classical
vectors obeying the Landau-Lifshitz-Gilbert equation and where their STT-driven
dynamics is initiated only when the spin-polarization of flowing electrons and
localized spins are noncollinear, quantum STT can occur when these vectors are
collinear but antiparallel. Using tDMRG, we simulate the time evolution of a
many-body quantum state of electrons and localized spins, where the former are
injected as a spin-polarized current pulse while the latter comprise a quantum
Heisenberg ferromagnetic metallic (FM) spin-$\frac{1}{2}$ XXZ chain initially
in the ground state with spin-polarization antiparallel to that of injected
electrons. The quantum STT reverses the direction of localized spins, but
without rotation from the initial orientation, when the number of injected
electrons exceeds the number of localized spins. Such nonclassical reversal,
which is absent from LLG dynamics, is strikingly inhomogeneous across the FM
chain and it can be accompanied by reduction of the magnetization associated
with localized spins, even to zero at specific locations. This is because
quantum STT generates a highly entangled nonequilibrium many-body state of all
flowing and localized spins, despite starting from the initially unentangled
ground state of a mundane FM. Furthermore, the mutual information between
localized spins at the FM edges remains nonzero even at infinite separation as
the signature of dynamical buildup of long-range entanglement.
