Localized Fock Space Cages in Kinetically Constrained Models

We investigate a mechanism for non-ergodic behavior in many-body quantum systems arising from destructive interference, leading to localization in Fock space. Drawing parallels with single-particle flat-band localization and Aharonov-Bohm cages, we identify conditions under which similar interference effects in the many-body domain produce Fock space cages (FSCs)-highly localized many-body eigenstates. By interpreting Fock space as a graph where nodes represent bitstring basis states and edges denote non-zero transition amplitudes of the Hamiltonian, we analyze different kinetically constrained models. The FSCs cause non-ergodic dynamics when the system is initialized within their support, highlighting a universal interference-driven localization mechanism in many-body systems.