Construction of Asymptotic Quantum Many-Body Scar States in the SU(N) Hubbard Model

We present an analytic construction of asymptotic quantum many-body scars (AQMBS) in one-dimensional SU(N) Hubbard chains. Our approach is based on a recent “parent-Hamiltonian” framework for AQMBS [1], in which the AQMBS states are obtained as low-lying gapless excited states of a parent Hamiltonian whose ground state is a quantum many-body scar (QMBS) state. The previous work [1] showed that the parent Hamiltonians of various models are related to the spin-1/2 ferromagnetic Heisenberg chain. In contrast, we show that the parent Hamiltonian of the SU(N) Hubbard chains, which possess QMBS states [2], reduces to the SU(N) ferromagnetic Heisenberg model. We analytically demonstrate that the system hosts AQMBS states, which can be identified with the magnon excitations of the SU(N) ferromagnetic Heisenberg model. Furthermore, we show the following properties [3]: (i) exact orthogonality to the QMBS, (ii) vanishing energy variance in the thermodynamic limit, and (iii) subvolume law entanglement, supported by rigorous MPS/MPO bounds.

[1] M. Kunimi et al., arXiv:2505.04853 (accepted for publication in Phys. Rev. Res.).

[2] M. Nakagawa et al., Phys. Rev. Res. 6, 043259 (2024).

[3] L. Gotta et al.,  Phys. Rev. Lett. 131, 190401 (2023).