Bipartite entanglement and surface criticality: The extra contribution of non-ordinary edge in entanglement

TL;DR

This paper investigates how boundary conditions and edge modes affect entanglement entropy in quantum critical systems, revealing that non-ordinary edges contribute additional gapless modes that influence entanglement measures.

Contribution

It connects many-body entanglement with surface criticality, demonstrating the impact of non-ordinary edges on entanglement entropy and clarifying the role of boundary conditions.

Findings

Ordinary bipartitions reflect bulk criticality accurately.

Non-ordinary edges contribute extra gapless modes affecting entanglement.

Entanglement spectrum approximately matches edge energy spectrum even at gapless points.

Abstract

Recent works on the scaling behaviors of entanglement entropy at the SO(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 work, 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.