Observation of entanglement spectrum signature for higher-order topology

Bulk-boundary correspondence is crucial for understanding topological insulators, as it indicates that nontrivial bulk topology can be revealed from the boundary response. However, not all topological insulators exhibit conventional energy or frequency boundary responses despite possessing a nontrivial bulk topology, which challenges the experimental probing of bulk topology. In this work, we utilize the entanglement spectrum, rather than the energy or frequency spectrum, for experimentally probing the bulk topology. We verify the bulk-entanglement spectrum correspondence in an acoustic multipole topological insulator even without the frequency boundary response. Our work provides a novel paradigm for probing the bulk topology and opens new avenues for exploring topological materials.