Defect-induced edge ferromagnetism and fractional spin excitations of the SU(4) $\pi$-flux Hubbard model on honeycomb lattice

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.