Ownerless island and partial entanglement entropy in island phases

TL;DR

This paper investigates the entanglement structure of island phases in 2D holographic models, introducing a generalized method for calculating partial entanglement entropy that accounts for ownerless islands and their role in entanglement wedge cross-sections.

Contribution

It proposes a new prescription for partial entanglement entropy in island phases, highlighting the significance of ownerless islands and their impact on entanglement measures.

Findings

Different ownerless island assignments yield different BPEs matching entanglement wedge cross-section saddles.

Minimizing BPE determines the optimal ownerless island assignment.

The geometric interpretation of PEE aligns with no-island phases in holography.

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.