  We study the dynamical properties of both bulk and edge spins of a
two-dimensional Affleck-Kennedy-Lieb-Tasaki (AKLT) model mainly by using the
stochastic series expansion quantum Monte Carlo method with stochastic analytic
continuation. In the deep AKLT phase, we obtain a spin spectrum with flat band,
which is a strong evidence for a localized state. Through the spectrum
analysis, we see a clear continuous phase transition from the AKLT phase to the
N\'eel phase in the model, and the energy gap becomes closed at the
corresponding momentum point. In comparison with linear spin-wave theory, the
differences show that there are strong interactions among magnons at high
energies. With open boundary condition, the gap of edge spins in the AKLT phase
closes at both the $\Gamma$ point and the $\pi$ point interestingly to emerge
into a flat-band-like Luttinger liquid phase, which can be explained by
symmetry and perturbation approximation. This paper helps us to better
understand the completely different dynamical behaviors of bulk and edge spins
in the symmetry protected topological phase.
