  The Motzkin and Fredkin quantum spin chains are described by frustration-free
Hamiltonians recently introduced and studied because of their anomalous
behaviors in the correlation functions and in the entanglement properties. In
this paper we analyze their quantum dynamical properties, focusing in
particular on the time evolution of the excitations driven by a quantum quench,
looking at the correlations functions of spin operators defined along different
directions, and discussing the results in relation with the cluster
decomposition property.
