Islands for Entanglement Negativity in Communicating Black Holes

We construct three models to describe the scenario where two eternal black holes are separated by a flat space, and can eventually be entangled by exchanging radiation. In the doubly holographic setup, we compute the entanglement entropy and mutual information among subsystems and obtain the dynamic phase structure of the entanglement. The formation of entanglement between these two black holes is delayed by the space which the radiation must travel through. If the black holes exchange sufficient Hawking modes, the final state is characterized by a connected entanglement wedge; otherwise, the final entanglement wedge contains two separate islands. In the former case, the entanglement wedge of the black holes forms at the time scale proportional to the size of the flat space between them. While in both cases, the unitarity of the evolution is preserved. When the sizes of the black holes are not equal, we observe a loss of entanglement between the smaller black hole and the radiation at late times. On the field theory side, we consider two Sachdev-Ye-Kitaev (SYK) clusters coupled to a Majorana chain, which resemble two black holes connected by a radiation region. We numerically compute the same entanglement measures and obtain similar phase structures as the bulk results. In general, a time delay of the entanglement between the SYK clusters is found in cases with a long Majorana chain. In particular, when the SYK clusters are different in size, similar entanglement loss between the smaller SYK cluster and the Majorana chain is observed. Finally, we investigate a chain model composed of EPR clusters with particles exchanging between neighboring clusters and reproduce the features of entanglement observed in the previous models.

Section: Conclusion and Discussionmentioning

confidence: 94%

“…Third, we will further simplify the model to be one composed of several EPR clusters which form a chain structure, with the outermost clusters being black holes and the inner clusters being radiation. See also [86][87][88] for other models in BCFT, BTZ black hole and black string with branes.…”

Section: Introductionmentioning

confidence: 99%

Black holes entangled by radiation

Liu

Xian

Peng

et al. 2022

“…proposed in quantum information theory [28][29][30][31][32] as well as for conformal field theories [32][33][34][35][36][37] and in holography [32,[38][39][40][41][42][43][44][45][46][47][48][49][50][51][52]. In [53], the authors have explored the model [23] and computed the holographic entanglement negativity for various bipartite mixed state configurations in the bath BCF T 2 s where the analogue of Page curves for the entanglement negativity was reproduced for communicating black holes, revealing some intriguing properties of the entanglement structure.…”

Section: Jhep02(2023)203mentioning

confidence: 99%

“…where S(X) is again the entanglement entropy for a interval X in the bath BCF T 2 s described in [53]. Let us now consider the different scenarios for the two disjoint intervals and compare the holographic reflected entropy with the mutual information.…”

Section: Disjoint Intervalsmentioning

confidence: 99%

Reflected entropy for communicating black holes. Part I. Karch-Randall braneworlds

Afrasiar

Basak

Chandra

et al. 2023

Self Cite

We obtain the reflected entropy for bipartite mixed state configurations of two adjacent and disjoint intervals at a finite temperature in BCFT2s with two distinct boundaries through a replica technique in the large central charge limit. Subsequently these field theory results are reproduced from bulk computations involving the entanglement wedge cross section in the dual BTZ black hole geometry truncated by two Karch-Randall branes. Our result confirms the holographic duality between the reflected entropy and the bulk entanglement wedge cross section in the context of the AdS3/BCFT2 scenario. We further investigate the critical issue of the holographic Markov gap between the reflected entropy and the mutual information for these configurations from the bulk braneworld geometry and study its variation with subsystem sizes and time.

“…This EOW brane is anchored to the BCFT boundary. This bottom-up model captures some qualitative aspects of stringy models for AdS/BCFT [7][8][9], and has served as a useful toy model for black hole evaporation [10][11][12][13][14][15][16][17][18][19][20][21], interpreted as doubly-holographic brane-world models [22][23][24][25]. On the other hand, this simplest model of AdS/BCFT is known to have several atypical features in the boundary operator spectrum amongst all holographic BCFTs, such as fine-tuned boundary operator spectrum [26] and the absence of interactions between distinct EOW branes.…”

Section: Introductionmentioning

confidence: 96%

Holographic BCFT with a Defect on the End-of-the-World brane

Miyaji

Murdia

2022

In this paper, we propose a new gravity dual for a 2d BCFT with two conformal boundaries by introducing a defect that connects the two End-of-the-World branes. We demonstrate that the BCFT dual to this bulk model exhibits a richer lowest spectrum. The corresponding lowest energy eigenvalue can continuously interpolate between $$ -\frac{\pi c}{24\Delta x} $$ − πc 24 Δ x and 0 where ∆x is the distance between the boundaries. This range was inaccessible to the conventional AdS/BCFT model with distinct boundary conditions. We compute the holographic entanglement entropy and find that it exhibits three different phases, one of which breaks the time reflection symmetry. We also construct a wormhole saddle, analogous to a 3d replica wormhole, which connects different boundaries through the AdS bulk. This saddle is present only if the BCFT is non-unitary and is always subdominant compared to the disconnected saddle.