Heat percolation in many-body flat-band localizing systems

We demonstrate robust ergodicity breaking in interacting many-body systems in arbitrary Euclidian dimension based on disorder-free many-body localization. Translationally invariant fine-tuned single-particle lattice Hamiltonians can host dispersionless (flat) bands only. Suitable short-range many-body interactions enforce complete suppression of particle transport due to local constraints and lead to ergodicity breaking termed many-body flat-band localization. However, heat might still flow between spatially locked charges. We demonstrate that heat transport is completely suppressed in one dimension. In higher dimensions we establish a universal bound on the filling fraction below which the heat transport is suppressed. The bound is based on the mapping to a classical percolation problem. Above the bound, the heat transport in percolation clusters is additionally affected by emerging bulk disorder and edge scattering induced by local constraints, which work in favor of arresting the heat flow and might keep the ergodicity breaking above the universal bound. We discuss explicit examples in one and two dimensions.