Nonlinear caging in all-bands-flat lattices

We study the impact of classical short-range nonlinear interactions on transport in lattices with no dispersion. The single particle band structure these contains flat bands only, and cages non-interacting particles into compact localized eigenstates. demonstrate that there always exist local unitary transformations detangle such decoupled sites dimension one. Starting from a detangled representation, inverting detangling entangling extending to higher lattice dimensions, we arrive at an All-Bands-Flat generator for states any dimension. are parametrized by sets angles. For given member set all-bands-flat, additional destroy caging general, induce transport. However, fine-tuned subsets allow completely restore caging. derive necessary sufficient fine-tuning conditions caging, provide computational evidence our conclusions one-dimensional systems.