Construction of asymptotic quantum many-body scar states in the SU($N$) Hubbard model

We construct asymptotic quantum many-body scars (AQMBS) in one-dimensional SU($N$) Hubbard chains ($N\geq 3$) by embedding the scar subspace into an auxiliary Hilbert subspace $\mathcal{H}_P$ and identifying a parent Hamiltonian within it, together with a corresponding extension of the restricted spectrum-generating algebra to the multi-ladder case. Unlike previous applications of the parent-Hamiltonian scheme, we show that the parent Hamiltonian becomes the SU($N$) ferromagnetic Heisenberg model rather than the spin-1/2 case, so that its gapless magnons realize explicit AQMBS of the original model. Working in the doublon-holon subspace, we derive this mapping, obtain the one-magnon dispersion for periodic and open boundaries, and prove (i) orthogonality to the scar states, (ii) vanishing energy variance in the thermodynamic limit, and (iii) subvolume entanglement entropy with rigorous MPS/MPO bounds. Our results broaden the parent-Hamiltonian family for AQMBS beyond spin-1/2 and provide analytic, low-entanglement excitations in SU($N$)-symmetric systems.