Ownerless island and partial entanglement entropy in island phases

Basu, Debarshi; Lin, Jiong; Lu, Yizhou; Wen, Qiang

doi:10.21468/SciPostPhys.15.6.227

SciPost Physics

Ownerless island and partial entanglement entropy in island phases

Debarshi Basu, Jiong Lin, Yizhou Lu, Qiang Wen

SciPost Phys. 15, 227 (2023) · published 6 December 2023

doi: 10.21468/SciPostPhys.15.6.227
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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. From a pure quantum information perspective, the entanglement islands emerge from the self-encoding property of the system, which gives us new insights on the construction of the PEE and the physical interpretation of two-point functions of twist operators in island phases. With the contributions from the entanglement islands properly 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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.6.227
TI  - Ownerless island and partial entanglement entropy in island phases
PY  - 2023/12/06
UR  - https://www.scipost.org/SciPostPhys.15.6.227
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 6
SP  - 227
A1  - Basu, Debarshi
AU  - Lin, Jiong
AU  - Lu, Yizhou
AU  - Wen, Qiang
AB  - 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. From a pure quantum information perspective, the entanglement islands emerge from the self-encoding property of the system, which gives us new insights on the construction of the PEE and the physical interpretation of two-point functions of twist operators in island phases. With the contributions from the entanglement islands properly 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.
ER  -

@Article{10.21468/SciPostPhys.15.6.227,
	title={{Ownerless island and partial entanglement entropy in island phases}},
	author={Debarshi Basu and Jiong Lin and Yizhou Lu and Qiang Wen},
	journal={SciPost Phys.},
	volume={15},
	pages={227},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.6.227},
	url={https://scipost.org/10.21468/SciPostPhys.15.6.227},
}

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¹ Debarshi Basu,
² ³ Jiong Lin,
⁴ Yizhou Lu,
⁵ Qiang Wen

Funders for the research work leading to this publication