Ownerless island and partial entanglement entropy in island phases

• URL: http://arxiv.org/abs/2305.04259v3
• Date: Wed, 6 Dec 2023 15:08:51 GMT
• Title: Ownerless island and partial entanglement entropy in island phases
• Authors: Debarshi Basu, Jiong Lin, Yizhou Lu and Qiang Wen
• Abstract summary: We study the entanglement structure of the island phases realized in several 2-dimensional holographic set-ups. The self-encoding property of the island phase changes the way we evaluate the partial entanglement entropy (PEE)
• Score: 8.157015066461513
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the context of partial entanglement entropy (PEE), we study the entanglement structure of the island phases realized in several 2-dimensional holographic set-ups. The self-encoding property of the island phase changes the way we evaluate the PEE. With the contributions from islands taken into account, we give a generalized prescription to construct PEE and balanced partial entanglement entropy (BPE). Here the ownerless island region, which lies inside the island $\text{Is}(AB)$ of $A\cup B$ but outside $\text{Is}(A)\cup \text{Is}(B)$, plays a crucial role. Remarkably, we find that under different assignments for the ownerless island, we get different BPEs, which exactly correspond to different saddles of the entanglement wedge cross-section (EWCS) in the entanglement wedge of $A\cup B$. The assignments can be settled by choosing the one that minimizes the BPE. Furthermore, under this assignment we study the PEE and give a geometric picture for the PEE in holography, which is consistent with the geometric picture in the no-island phases.

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