Statistical localization of U(1) lattice gauge theory in a Rydberg simulator

Lattice gauge theories provide a framework for describing dynamical systems ranging from nuclei to materials. When they host concatenated conservation laws, their Hilbert space can fragment into subspaces labelled by non-local quantities—a phenomenon known as Hilbert space fragmentation. Although non-local conservation laws are expected not to hinder local thermalization, this assumption has been questioned by the idea of statistical localization, where motifs of microscopic configurations remain frozen owing to strong fragmentation. Here we observe experimental signatures of such behaviour in a constrained lattice gauge theory using a facilitated Rydberg-atom array, where atoms mediate the dynamics of charge clusters whose non-local net-charge patterns remain invariant. By reconstructing observables sampled over time, we probe the spatial distribution of conserved quantities. We find that strong Hilbert space fragmentation keeps these quantities locally distributed in typical quantum states, even though they are defined by non-local string-like operators. This establishes a setting for high-energy studies of cluster dynamics and low-energy investigations of strong zero modes that persist in infinite-temperature topological systems.