  The relaxation of a classical spin, exchange coupled to the local magnetic
moment at an edge site of the one-dimensional spinful Su-Schrieffer-Heeger
model is studied numerically by solving the full set of equations of motion. A
Lindblad coupling of a few sites at the opposite edge to an absorbing bath
ensures that convergence with respect to the system size is achieved with only
a moderate number of core sites. This allows us to numerically exactly study
the long-time limit and to determine the parameter regimes where spin
relaxation takes place. Corresponding dynamical phase diagrams for the
topologically trivial and the nontrivial cases are constructed. The dynamical
phase boundaries, the role of the topological edge state and its internal
Zeeman splitting for the spin-relaxation process, as well as incomplete spin
relaxation on long time scales can be explained within the framework of a
renormalized linear-response approach when explicitly taking retardation
effects and nonequilibrium spin-exchange processes into account.
