Random tensor networks with nontrivial links

Cheng, Newton; Lancien, Cécilia; Penington, Geoff; Walter, Michael; Witteveen, Freek

doi:10.48550/arxiv.2206.10482

Cited by 2 publications

(4 citation statements)

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“…domain walls with tensions modified by the entanglement spectrum, thus introducing an m dependence [8,23]. For m ≥ 2, we have…”

Section: Discussionmentioning

confidence: 99%

“…One may consider a simple deformation of the above model, by changing the maximally entangled legs of the RTN to non-maximally entangled legs. Such states have also been useful to model holographic states [23]. In fact, the simplest situation where we add non-maximal entanglement to the C leg results in a state identical to the PSSY model of black hole evaporation [24].…”

Section: Examplesmentioning

confidence: 99%

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Reflected entropy in random tensor networks

Akers

Faulkner

Lin

et al. 2022

J. High Energ. Phys.

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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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“…domain walls with tensions modified by the entanglement spectrum, thus introducing an m dependence [8,23]. For m ≥ 2, we have…”

Section: Discussionmentioning

confidence: 99%

Section: Examplesmentioning

confidence: 99%

Reflected entropy in random tensor networks

Akers

Faulkner

Lin

et al. 2022

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…In some cases the distinction between the two is blurred by quantum scars [65]. One proposal to build more realistic holographic tensor networks is to use random tensors with nontrivial links [17]. However, in our model, upgrading the tensor network (figure 2) to the exact CFT state (3.3) does not appear to be as simple as weighting the tensors.…”

Section: Higher Dimensions: Beyond Spherical Symmetrymentioning

confidence: 95%

“…A quantum state constructed from a random tensor network has an entanglement structure dictated by the geometry of the network, and satisfies a discrete version of the Ryu-Takayanagi formula [1][2][3]. There are arguments that a tensor network can be constructed from the bulk theory in principle [4][5][6][7][8], and further connections have been developed in, e.g, [9][10][11][12][13][14][15][16][17][18][19][20]. This is closely related to the idea that spacetime can be understood as a quantum errorcorrecting code [2,[21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Toward random tensor networks and holographic codes in CFT

Chandra¹,

Hartman²

2023

Preprint

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In holographic CFTs satisfying eigenstate thermalization, there is a regime where the operator product expansion can be approximated by a random tensor network. The geometry of the tensor network corresponds to a spatial slice in the holographic dual, with the tensors discretizing the radial direction. In spherically symmetric states in any dimension and more general states in 2d CFT, this leads to a holographic error-correcting code, defined in terms of OPE data, that can be systematically corrected beyond the random tensor approximation. The code is shown to be isometric for light operators outside the horizon, and non-isometric inside, as expected from general arguments about bulk reconstruction. The transition at the horizon occurs due to a subtle breakdown of the Virasoro identity block approximation in states with a complex interior.

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Random tensor networks with nontrivial links

Cited by 2 publications

References 0 publications

Reflected entropy in random tensor networks

Reflected entropy in random tensor networks

Toward random tensor networks and holographic codes in CFT

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