Interaction-driven breakdown of Aharonov--Bohm caging in flat-band Rydberg lattices

Flat bands play a central role in hosting emergent states of matter in many condensed matter systems, from the nascent insulating states of twisted bilayer graphene to the fractionalized excitations found in frustrated magnets and quantum Hall materials. Here, we report on the experimental realization of highly tunable flat-band models populated by strongly interacting Rydberg atoms. Using the approach of synthetic dimensions, we engineer a flat-band rhombic lattice with twisted boundaries, and through nonequilibrium dynamics we explore the control of Aharonov--Bohm (AB) caging via a tunable $U(1)$ gauge field. Through microscopic measurements of Rydberg pairs, we explore the interaction-driven breakdown of AB caging in the limit of strong dipolar interactions that mix the lattice bands. In the limit of weak interactions, where caging remains intact, we observe an effective magnetism that arises due to the interaction-driven mixing of degenerate flat-band states. These observations of strongly correlated flat-band dynamics open the door to explorations of new emergent phenomena in synthetic quantum materials.