Built on

J. Kudler-Flam, I. MacCormack and S. Ryu, “Holographic entanglement contour, bit threads, and the entanglement tsunami,” J. Phys. A 52
Original
1902
Earlier work this paper cites.
G. ’t Hooft, “A Planar Diagram Theory for Strong Interactions,” Nucl. Phys. B 72
1974
Earlier work this paper cites.
J. M. Maldacena, “The Large N limit of superconformal field theories and supergravity,” Int. J. Theor. Phys. 38
1998
Earlier work this paper cites.
S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
G. Vidal, “Entanglement Renormalization,” Phys. Rev. Lett. 99
2008
Earlier work this paper cites.
D.Calegari, M.Freedman, K.Walker, “positivity of the universal pairing in 3 dimensions,” Jour. Amer. Math. Soc. 23 (2010), no. 1, 107-188 [arXiv:0802.3208]
Original
2010
Earlier work this paper cites.
M. Van Raamsdonk, “Building up spacetime with quantum entanglement,” Gen. Rel. Grav. 42
Original
2010
Earlier work this paper cites.
B. Swingle, “Entanglement Renormalization and Holography,” Phys. Rev. D 86
Original
2012
Earlier work this paper cites.
M. Nozaki, S. Ryu and T. Takayanagi, “Holographic Geometry of Entanglement Renormalization in Quantum Field Theories,” JHEP 1210
Original
2012
Earlier work this paper cites.
J. Haegeman, T. J. Osborne, H. Verschelde and F. Verstraete, “Entanglement Renormalization for Quantum Fields in Real Space,” Phys. Rev. Lett. 110
Original
2013
Earlier work this paper cites.

Similar

C. Bény, “Causal structure of the entanglement renormalization ansatz,” New J. Phys. 15
Original
2013
Cited alongside, same era.
T. Faulkner, A. Lewkowycz and J. Maldacena, “Quantum corrections to holographic entanglement entropy,” JHEP 1311
Original
2013
Cited alongside, same era.
M. Nozaki, T. Numasawa and T. Takayanagi, “Holographic Local Quenches and Entanglement Density,” JHEP 1305
Original
2013
Cited alongside, same era.
Y. Chen and G. Vidal, “Entanglement contour”, J. Stat. Mech. Vol. 2014, P10011 (2014) [arXiv:1406.1471 [cond-mat]]
Original
2014
Cited alongside, same era.
B. Czech, L. Lamprou, S. McCandlish and J. Sully, “Integral Geometry and Holography,” JHEP 1510

Then

C. T. Asplund, N. Callebaut and C. Zukowski, “Equivalence of Emergent de Sitter Spaces from Conformal Field Theory,” JHEP 1609
Original
2016
Later among the works it cites.
G.Vidal, “Tensor networks for quantum fields: Conformal invariance and emergent de sitter space,” It for Qubit School, Perimeter Insitute, 2016
2016
Later among the works it cites.
P. Hayden, S. Nezami, X. L. Qi, N. Thomas, M. Walter and Z. Yang, “Holographic duality from random tensor networks,” JHEP 1611
Original
2016
Later among the works it cites.
M. Freedman and M. Headrick, “Bit threads and holographic entanglement,” Commun. Math. Phys. 352
Original
2017
Later among the works it cites.
I. Bakhmatov, N. S. Deger, J. Gutowski, E. ó. Colgáin and H. Yavartanoo, JHEP 1707

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2018

Quantum bit threads of MERA tensor network in large $c$ limit

Chen, Chong-Bin, Shu, Fu-Wen, Wu, Meng-He

Understand

The Ryu-Takayanagi (RT) formula is a crucial concept in current theory of gauge-gravity duality and emergent phenomena of geometry.

Recent reinterpretation of this formula in terms of a set of "bit threads" is an interesting effort in understanding holography.
In this paper, we investigate a quantum generalization of the "bit threads" based on tensor network, with particular interests in the multi-scale entanglement renormalization ansatz (MERA).
We demonstrate that, in the large $c$ limit, isometries of the MERA can be regarded as "sources" (or "sinks") of the information flow, which extensively modifies the original picture of the bit threads by introducing a new variable $\rho$: density of the isometries.

Built on

J. Kudler-Flam, I. MacCormack and S. Ryu, “Holographic entanglement contour, bit threads, and the entanglement tsunami,” J. Phys. A 52
Original
1902
Earlier work this paper cites.
G. ’t Hooft, “A Planar Diagram Theory for Strong Interactions,” Nucl. Phys. B 72
1974
Earlier work this paper cites.
J. M. Maldacena, “The Large N limit of superconformal field theories and supergravity,” Int. J. Theor. Phys. 38
1998
Earlier work this paper cites.
S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
G. Vidal, “Entanglement Renormalization,” Phys. Rev. Lett. 99
2008
Earlier work this paper cites.
D.Calegari, M.Freedman, K.Walker, “positivity of the universal pairing in 3 dimensions,” Jour. Amer. Math. Soc. 23 (2010), no. 1, 107-188 [arXiv:0802.3208]
Original
2010
Earlier work this paper cites.
M. Van Raamsdonk, “Building up spacetime with quantum entanglement,” Gen. Rel. Grav. 42
Original
2010
Earlier work this paper cites.
B. Swingle, “Entanglement Renormalization and Holography,” Phys. Rev. D 86
Original
2012
Earlier work this paper cites.
M. Nozaki, S. Ryu and T. Takayanagi, “Holographic Geometry of Entanglement Renormalization in Quantum Field Theories,” JHEP 1210
Original
2012
Earlier work this paper cites.
J. Haegeman, T. J. Osborne, H. Verschelde and F. Verstraete, “Entanglement Renormalization for Quantum Fields in Real Space,” Phys. Rev. Lett. 110
Original
2013
Earlier work this paper cites.

Similar

C. Bény, “Causal structure of the entanglement renormalization ansatz,” New J. Phys. 15
Original
2013
Cited alongside, same era.
T. Faulkner, A. Lewkowycz and J. Maldacena, “Quantum corrections to holographic entanglement entropy,” JHEP 1311
Original
2013
Cited alongside, same era.
M. Nozaki, T. Numasawa and T. Takayanagi, “Holographic Local Quenches and Entanglement Density,” JHEP 1305
Original
2013
Cited alongside, same era.
Y. Chen and G. Vidal, “Entanglement contour”, J. Stat. Mech. Vol. 2014, P10011 (2014) [arXiv:1406.1471 [cond-mat]]
Original
2014
Cited alongside, same era.
B. Czech, L. Lamprou, S. McCandlish and J. Sully, “Integral Geometry and Holography,” JHEP 1510

Then

C. T. Asplund, N. Callebaut and C. Zukowski, “Equivalence of Emergent de Sitter Spaces from Conformal Field Theory,” JHEP 1609
Original
2016
Later among the works it cites.
G.Vidal, “Tensor networks for quantum fields: Conformal invariance and emergent de sitter space,” It for Qubit School, Perimeter Insitute, 2016
2016
Later among the works it cites.
P. Hayden, S. Nezami, X. L. Qi, N. Thomas, M. Walter and Z. Yang, “Holographic duality from random tensor networks,” JHEP 1611
Original
2016
Later among the works it cites.
M. Freedman and M. Headrick, “Bit threads and holographic entanglement,” Commun. Math. Phys. 352
Original
2017
Later among the works it cites.
I. Bakhmatov, N. S. Deger, J. Gutowski, E. ó. Colgáin and H. Yavartanoo, JHEP 1707

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2015

Cited alongside, same era.

F. Pastawski, B. Yoshida, D. Harlow and J. Preskill, “Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence,” JHEP 1506

Original

2015

Cited alongside, same era.

N. Bao, C. J. Cao, S. M. Carroll, A. Chatwin-Davies, N. Hunter-Jones, J. Pollack and G. N. Remmen, “Consistency conditions for an AdS multiscale entanglement renormalization ansatz correspondence,” Phys. Rev. D 91

Original

2015

Cited alongside, same era.

S. X. Cui, M. H. Freedman, O. Sattath, R. Stong and G. Minton, “Quantum Max-flow/Min-cut,” J. Math. Phys. 57

Original

2016

Cited alongside, same era.

B. Czech, L. Lamprou, S. McCandlish and J. Sully, “Tensor Networks from Kinematic Space,” JHEP 1607

Original

2016

Cited alongside, same era.

J. de Boer, M. P. Heller, R. C. Myers and Y. Neiman, “Holographic de Sitter Geometry from Entanglement in Conformal Field Theory,” Phys. Rev. Lett. 116

Original

2016

Cited alongside, same era.

Properly speaking, it refers to a special tensor network—the multi-scale entanglement renormalization ansatz (MERA) which was introduced in vidal

Cited in the paper.

In this article we all consider the continuous MERA(cMERA) case instead of the lattice MERA case. We all just use “MERA” to denote the continuous case. The definition of cMERA can be found in Haegeman:2011uy . Therefore the emerged spacetime is a Lorentzian manifold

Cited in the paper.

Original

2017

Later among the works it cites.

M. Miyaji, T. Takayanagi and K. Watanabe, “From path integrals to tensor networks for the AdS/CFT correspondence,” Phys. Rev. D 95

Original

2017

Later among the works it cites.

W. Gan and F. Shu, “Holography as deep learning,” Int. J. Mod. Phys. D 26

Original

2017

Later among the works it cites.