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We study quantum quenches in the $S=1$ Heisenberg spin chain and show thatthe dynamics can be described by the recently developed semi-semiclassicalmethod based on particles propagating along classical trajectories butscattering quantum mechanically. We analyze the non-equilibrium time evolutionof the distribution of the total spin in half of the system and compare thepredictions of the semi-semiclassical theory with those of a non-Abelian timeevolving block decimation (TEBD) algorithm which exploits the SU(2) symmetry.We show that while the standard semiclassical approach using the universal lowenergy scattering matrix cannot describe the dynamics, the hybrid semiclassicalmethod based on the full scattering matrix gives excellent agreement with thefirst principles TEBD simulation.

Spin fluctuations after quantum quenches in the S=1 Haldane chain: numerical validation of the semi-semiclassical theory