Emergent localization in locally perturbed fragmented systems

We investigate the robustness of constrained quantum systems exhibiting Hilbert space fragmentation with respect to local perturbations that break the constraints. We consider both random unitary dynamics and Hamiltonian evolution. For random unitary dynamics, the constraint-breaking perturbations lead to rapid destruction of Hilbert space fragmentation, with states quickly spreading out over all of Hilbert space. Under Hamiltonian dynamics however, the system still exhibits an effective form of Hilbert space fragmentation, with the dynamics retaining memory of its initial state for extremely long times.