  Recently, a SU(4) $\pi$-flux Hubbard model on the honeycomb lattice has been
proposed to study the spin-orbit excitations of $\alpha$-ZrCl$_3$
[Phys.~Rev.~Lett. 121.097201~(2017)]. Based on this model with a zigzag edge,
we show the edge defects can induce edge flat bands that result in a SU(4) edge
ferromagnetism. We develop an effective one-dimensional interaction Hamiltonian
to study the corresponding SU(4) spin excitations. Remarkably, SU(4) spin
excitations of the edge ferromagnet appear as a continuum covering the entire
energy region rather than usual magnons. Through further entanglement entropy
analysis, we suggest that the continuum consists of fractionalized spin
excitations from the disappeared magnons, except for that from the
particle-hole Stoner excitations. Moreover, in ribbon systems with finite
widths, the disappeared magnons can be restored in the gap formed by the
finite-size effect and the optical branch of the restored magnons are found to
be topological nontrivial.
