  We study a quantum spin Kitaev model with zigzag edges to clarify the effects
of anisotropy in the exchange couplings on the spin propagation. We simulate
the spin and Majorana dynamics triggered by a magnetic pulse, using the
real-space time-dependent Majorana mean-field theory. When the anisotropy is
small, the dispersion of the itinerant Majorana fermions remains gapless, where
the velocity of the spin propagation matches the group velocity of the
itinerant Majorana fermions at the nodal points. On the other hand, in the
gapped system with a large anisotropy, the spin propagation is strongly
suppressed although its nature depends on the shape of the pulse. The spin
transport in the junction system described by the Kitaev models with distinct
anisotropies is also dressed.
