Replica Wormholes and Holographic Entanglement Negativity

Dong, Xi; McBride, Sean; Weng, Wayne W.

doi:10.48550/arxiv.2110.11947

Cited by 14 publications

(23 citation statements)

References 23 publications

(43 reference statements)

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“…Because there is no common geodesic element between all three elements (that is Γ(g A , e) ∩ Γ(g B , e) ∩ Γ(g A , g B ) is empty), there is no simple argument that determines the phase in this region. 7 This is the main difference between our calculation and the negativity computations in [26,33,34]. Instead we must seek other methods for determining the phase in this region.…”

Section: Phase Diagram and Rényi Reflected Entropiesmentioning

confidence: 99%

“…It was recently applied to find the entanglement entropy of JT gravity [25] and generic fixed area states [24]. Similar techniques were used to calculate the negativity [33,48]. This powerful approach enables us to write down the Schwinger-Dyson equation for the resolvent of ρ AB , which then gives full information about the entanglement spectrum.…”

Section: Schwinger-dyson For Entanglement Entropymentioning

confidence: 99%

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Reflected entropy in random tensor networks

Akers,

Faulkner,

Lin

et al. 2021

Preprint

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In holographic theories, the reflected entropy has been shown to be dual to the area of the entanglement wedge cross section. We study the same problem in random tensor networks demonstrating an equivalent duality. For a single random tensor we analyze the important non-perturbative effects that smooth out the discontinuity in the reflected entropy across the Page phase transition. By summing over all such effects, we obtain the reflected entanglement spectrum analytically, which agrees well with numerical studies. This motivates a prescription for the analytic continuation required in computing the reflected entropy and its Rényi generalization which resolves an order of limits issue previously identified in the literature. We apply this prescription to hyperbolic tensor networks and find answers consistent with holographic expectations. In particular, the random tensor network has the same non-trivial tripartite entanglement structure expected from holographic states. We furthermore show that the reflected Rényi spectrum is not flat, in sharp contrast to the usual Rényi spectrum of these networks. We argue that the various distinct contributions to the reflected entanglement spectrum can be organized into approximate superselection sectors. We interpret this as resulting from an effective description of the canonically purified state as a superposition of distinct tensor network states. Each network is constructed by doubling and gluing various candidate entanglement wedges of the original network. The superselection sectors are labelled by the different cross-sectional areas of these candidate entanglement wedges.

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Section: Phase Diagram and Rényi Reflected Entropiesmentioning

confidence: 99%

Section: Schwinger-dyson For Entanglement Entropymentioning

confidence: 99%

Reflected entropy in random tensor networks

Akers,

Faulkner,

Lin

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…It would be interesting to generalize this formalism to non-Abelian symmetry groups and systems with local symmetry constraints such as in the gauge theories and anyon chains [114] and possibly pinpoint the differences. Recently, the entanglement negativity of random tensor networks [22,23,26] was investigated. Given the dramatic effects of global symmetries on entanglement properties of single tensors (which was studied in the current work), it may be worth exploring which universal properties in random tensor networks would change in the presence of global symmetries.…”

Section: Discussionmentioning

confidence: 99%

“…[11] was introduced and employed to calculate the entanglement negativity and the entanglement negativity spectrum in the setting outlined above (see also Refs. [22][23][24][25][26] for a similar diagrammatic approach to the entanglement negativity and relative entropy of random tensor networks and models of evaporating black holes); it was shown that the main parameter controlling the entanglement behavior is q = L B L A , where L s denotes the Hilbert space dimension of s = A, B. Looking at extreme limits of this parameter is illuminating: for q 1 one expects the bath to be very large and thus A to be almost fully entangled with B resulting in a minimal entanglement between A 1 and A 2 .…”

Section: Introductionmentioning

confidence: 99%

Symmetry protected entanglement in random mixed states

Hejazi¹,

Shapourian²

2021

Preprint

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Symmetry is an important property of quantum mechanical systems which may dramatically influence their behavior in and out of equilibrium. In this paper, we study the effect of symmetry on tripartite entanglement properties of typical states in symmetric sectors of Hilbert space. In particular, we consider Abelian symmetries and derive an explicit expression for the logarithmic entanglement negativity of systems with ZN and U (1) symmetry groups. To this end, we develop a diagrammatic method to incorporate partial transpose within the random matrix theory of symmetric states and formulate a perturbation theory in the inverse of the Hilbert space dimension. We further present entanglement phase diagrams as the subsystem sizes are varied and show that there are qualitative differences between systems with and without symmetries. We also design a quantum circuit to simulate our setup.

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“…The technique we use here was presented in Ref. [5] (see also [23][24][25]). This powerful approach enables us to write down a Schwinger-Dyson equation for the resolvent of ρ R 1 R 2 , which then gives full information about the entanglement spectrum.…”

Section: Resolvent Trickmentioning

confidence: 99%

The Page Curve for Reflected Entropy

Akers,

Faulkner,

Lin

et al. 2022

Preprint

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We study the reflected entropy S R in the West Coast Model, a toy model of black hole evaporation consisting of JT gravity coupled to end-of-the-world branes. We demonstrate the validity of the holographic duality relating it to the entanglement wedge cross section away from phase transitions. Further, we analyze the important non-perturbative effects that smooth out the discontinuity in the S R phase transition. By performing the gravitational path integral, we obtain the reflected entanglement spectrum analytically. The spectrum takes a simple form consisting of superselection sectors, which we interpret as a direct sum of geometries, a disconnected one and a connected one involving a closed universe. We find that area fluctuations of O( √ G N ) spread out the S R phase transition in the canonical ensemble, analogous to the entanglement entropy phase transition. We also consider a Renyi generalization of the reflected entropy and show that the location of the phase transition varies as a function of the Renyi parameter.

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Replica Wormholes and Holographic Entanglement Negativity

Cited by 14 publications

References 23 publications

Reflected entropy in random tensor networks

Reflected entropy in random tensor networks

Symmetry protected entanglement in random mixed states

The Page Curve for Reflected Entropy

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