Localized Fock space cages in kinetically constrained models

We investigate a mechanism for nonergodic behavior arising from destructive interference in Fock space, leading to Fock space cages (FSCs)—exact zero-energy eigenstates localized on O(1) to O(L^p) configurations within an exponentially large connected Krylov sector. Unlike many-body localization or Hilbert space fragmentation, FSCs emerge from graph-theoretic interference cancellations in disorder-free kinetically constrained systems with chiral symmetry. We develop systematic algorithms that enable explicit construction of these cages in four representative models, revealing this as a universal mechanism for kinetically constrained systems with chiral symmetry. Dynamically, FSCs produce persistent plateaus in the Loschmidt echo and magnetization: return probabilities scale as L⁻² for O(L) cages and remain O(1) for ultralocal ones, while the magnetization saturates to O(1) instead of decaying to zero. This may provide new routes for engineering long-lived nonthermal states in quantum simulation platforms.