Quasi-Nambu-Goldstone modes in many-body scar models

From the quasisymmetry-group perspective [Phys. Rev. Lett. 126, 120604 (2021)], we show the universal existence of collective, coherent modes of excitations with small momenta in many-body scar models in the degenerate limit, where the energy spacing in the scar tower vanishes. The number of these modes, as well as the quantum numbers carried by them, are given, not by the symmetry of the Hamiltonian, but by the quasisymmetry of the scar tower: hence the name quasi-Goldstone modes. Based on this, we draw a concrete analogy between the paradigm of spontaneous symmetry breaking and the many-body scar physics in the degenerate limit.