Bipartite Entanglement and Surface Criticality: The Extra Contribution of the Nonordinary Edge in Entanglement

Recent works on the scaling behaviors of entanglement entropy at the S⁢O⁡(5) deconfined quantum critical point (DQCP) sparked a huge controversy. Different bipartitions gave out totally different conclusions for whether the DQCP is consistent with a unitary conformal field theory. In this Letter, we connect two previously disconnected fields—the many-body entanglement and the surface criticality—to reveal the behaviors of entanglement entropy in various bipartite scenarios, and point out that only the ordinary bipartition purely reflects the criticality of the bulk; otherwise, the extra gapless edge mode will also contribute to the entanglement. We have demonstrated that the correspondence between the entanglement spectrum and the edge energy spectrum still approximately persists even at a bulk-gapless point, thereby influencing the behavior of entanglement entropy. Our results establish that boundary conditions induced by the cut are decisive for entanglement-based probes and provide practical protocols to separate bulk from boundary contributions.