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arXiv · 2305.04259

Ownerless island and partial entanglement entropy in island phases

Debarshi Basu·Jiong Lin·Yizhou Lu·Qiang Wen
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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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Debarshi Basu, Jiong Lin, Yizhou Lu, Qiang Wen. 2023-05-07. Ownerless island and partial entanglement entropy in island phases. https://doi.org/10.21468/scipostphys.15.6.227

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