Partial entanglement entropy threads in the island phase

Abstract

In the context of the AdS/CFT, it was recently proposed that the boundary partial entanglement entropy structure can be represented by the so-called partial entanglement entropy (PEE) threads in the AdS bulk, which are bulk geodesics with the density determined by the boundary PEE structure [. and .]. In Poincaré anti–de Sitter (AdS) space, it was shown that the PEE threads cover the AdS space uniformly, such that the number of intersections between any bulk surface and the bulk PEE threads is always given by the area of the surface divided by 4G. In this paper, we investigate the configurations of PEE threads when the boundary state is in the island phase. The island phase was studied in the context of the holographic Weyl transformed CFT2, which has been shown to capture all the main features of AdS/BCFT (Boundary Conformal Field Theory). Compared with AdS3/CFT2, in the island phase instead of modifying the distribution of the bulk PEE threads, we should replace the boundary points with the corresponding cutoff spheres. Then the two-point functions and the four-point functions of twist operators can be reproduced by identifying the bulk homologous surfaces anchored on the corresponding cutoff spheres that has the minimal number of intersections with the bulk PEE threads. This gives us a better understanding about the PEE structure in the island phase and reproduces the island formula for entanglement entropy by allowing homologous surfaces to anchor on any cutoff spheres. Furthermore, it gives a demonstration for the two basic proposals and a better understanding for the entanglement contribution that makes the foundation to compute the balanced partial entanglement entropy [.], which reproduces the entanglement wedge cross section in the island phase. Published by the American Physical Society 2025