Built on

P. Erdős, P. Erdős, and A. Rényi, On the Evolution of Random Graphs, Publ. Math. Inst. HUNGARIAN Acad. Sci. , 17 (1960)
1960
Earlier work this paper cites.
J. Cheeger, A lower bound for the smallest eigenvalue of the laplacian, in Proceedings of the Princeton conference in honor of Professor S. Bochner (1969) pp. 195–199
1969
Earlier work this paper cites.
N. Alon, Eigenvalues and expanders, Combinatorica 6
1986
Earlier work this paper cites.
S. Sachdev and J. Ye, Gapless spin-fluid ground state in a random quantum Heisenberg magnet, Phys. Rev. Lett. 70
1993
Earlier work this paper cites.
S. Lloyd, Universal Quantum Simulators, Science (80-. ). 273
1996
Earlier work this paper cites.
S. B. Bravyi and A. Y. Kitaev, Fermionic Quantum Computation, Ann. Phys. (N. Y). 298
2002
Earlier work this paper cites.
J. Friedman, A proof of alon’s second eigenvalue conjecture, in Proc. thirty-fifth ACM Symp. Theory Comput. - STOC ’03 (ACM Press, New York, New York, USA, 2003) p. 720
2003
Earlier work this paper cites.
P. Hayden and J. Preskill, Black holes as mirrors: quantum information in random subsystems, J. High Energy Phys. 2007
Original
2007
Earlier work this paper cites.
Y. Sekino and L. Susskind, Fast scramblers, J. High Energy Phys. 2008
Original
2008
Earlier work this paper cites.
W. Brown and O. Fawzi, Scrambling speed of random quantum circuits, arXiv:1210.6644 (2012)
Original
2012
Earlier work this paper cites.
N. Lashkari, D. Stanford, M. Hastings, T. Osborne, and P. Hayden, Towards the fast scrambling conjecture, J. High Energy Phys. 2013
Original
2013
Earlier work this paper cites.
S. H. Shenker and D. Stanford, Black holes and the butterfly effect, J. High Energy Phys. 2014
2014
Earlier work this paper cites.
A. Kitaev, A simple model of quantum holography, in KITP Program: Entanglement Strongly-Correlated Quantum Matter (2015)
2015
Earlier work this paper cites.
S. Sachdev, Bekenstein-hawking entropy and strange metals, Phys. Rev. X 5
2015
Earlier work this paper cites.
M. Blake, Universal charge diffusion and the butterfly effect in holographic theories, Phys. Rev. Lett. 117
2016
Earlier work this paper cites.
P. Hosur, X.-L. Qi, D. A. Roberts, and B. Yoshida, Chaos in quantum channels, J. High Energy Phys. 2016
Original
2016
Earlier work this paper cites.
J. Polchinski and V. Rosenhaus, The spectrum in the Sachdev-Ye-Kitaev model, J. High Energy Phys. 2016
Original
2016
Earlier work this paper cites.

Similar

J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94
Original
2016
Cited alongside, same era.
J. Maldacena, S. H. Shenker, and D. Stanford, A bound on chaos, J. High Energy Phys. 2016
2016
Cited alongside, same era.
W. Fu, D. Gaiotto, J. Maldacena, and S. Sachdev, Supersymmetric SYK models, Phys. Rev. D 95
Original
2016
Cited alongside, same era.
R. Gurau, The complete 1/N expansion of a SYK–like tensor model, Nucl. Phys. B 916
Original
2017
Cited alongside, same era.
Y. Gu, X.-L. Qi, and D. Stanford, Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models, J. High Energy Phys. 2017
2017
Cited alongside, same era.

Then

E. Witten, An SYK-like model without disorder, J. Phys. A Math. Theor. 52
2019
Later among the works it cites.
A. W. Harrow, L. Kong, Z.-W. Liu, S. Mehraban, and P. W. Shor, A separation of out-of-time-ordered correlator and entanglement, arXiv:1906.02219 (2019)
Original
2019
Later among the works it cites.
C.-F. Chen and A. Lucas, Operator growth bounds from graph theory, arXiv:1905.03682 (2019)
Original
2019
Later among the works it cites.
A. R. Brown, H. Gharibyan, S. Leichenauer, H. W. Lin, S. Nezami, G. Salton, L. Susskind, B. Swingle, and M. Walter, Quantum gravity in the lab: Teleportation by size and traversable wormholes, arXiv:1911.06314 (2019)
Original
2019
Later among the works it cites.
R. Babbush, D. W. Berry, and H. Neven, Quantum simulation of the Sachdev-Ye-Kitaev model by asymmetric qubitization, Phys. Rev. A 99

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2020

A Sparse Model of Quantum Holography

Xu, Shenglong, Susskind, Leonard, Su, Yuan et al.

Understand

We study a sparse version of the Sachdev-Ye-Kitaev (SYK) model defined on random hypergraphs constructed either by a random pruning procedure or by randomly sampling regular hypergraphs.

The resulting model has a new parameter, $k$, defined as the ratio of the number of terms in the Hamiltonian to the number of degrees of freedom, with the sparse limit corresponding to the thermodynamic limit at fixed $k$.
We argue that this sparse SYK model recovers the interesting global physics of ordinary SYK even when $k$ is of order unity.
In particular, at low temperature the model exhibits a gravitational sector which is maximally chaotic.

Built on

P. Erdős, P. Erdős, and A. Rényi, On the Evolution of Random Graphs, Publ. Math. Inst. HUNGARIAN Acad. Sci. , 17 (1960)
1960
Earlier work this paper cites.
J. Cheeger, A lower bound for the smallest eigenvalue of the laplacian, in Proceedings of the Princeton conference in honor of Professor S. Bochner (1969) pp. 195–199
1969
Earlier work this paper cites.
N. Alon, Eigenvalues and expanders, Combinatorica 6
1986
Earlier work this paper cites.
S. Sachdev and J. Ye, Gapless spin-fluid ground state in a random quantum Heisenberg magnet, Phys. Rev. Lett. 70
1993
Earlier work this paper cites.
S. Lloyd, Universal Quantum Simulators, Science (80-. ). 273
1996
Earlier work this paper cites.
S. B. Bravyi and A. Y. Kitaev, Fermionic Quantum Computation, Ann. Phys. (N. Y). 298
2002
Earlier work this paper cites.
J. Friedman, A proof of alon’s second eigenvalue conjecture, in Proc. thirty-fifth ACM Symp. Theory Comput. - STOC ’03 (ACM Press, New York, New York, USA, 2003) p. 720
2003
Earlier work this paper cites.
P. Hayden and J. Preskill, Black holes as mirrors: quantum information in random subsystems, J. High Energy Phys. 2007
Original
2007
Earlier work this paper cites.
Y. Sekino and L. Susskind, Fast scramblers, J. High Energy Phys. 2008
Original
2008
Earlier work this paper cites.
W. Brown and O. Fawzi, Scrambling speed of random quantum circuits, arXiv:1210.6644 (2012)
Original
2012
Earlier work this paper cites.
N. Lashkari, D. Stanford, M. Hastings, T. Osborne, and P. Hayden, Towards the fast scrambling conjecture, J. High Energy Phys. 2013
Original
2013
Earlier work this paper cites.
S. H. Shenker and D. Stanford, Black holes and the butterfly effect, J. High Energy Phys. 2014
2014
Earlier work this paper cites.
A. Kitaev, A simple model of quantum holography, in KITP Program: Entanglement Strongly-Correlated Quantum Matter (2015)
2015
Earlier work this paper cites.
S. Sachdev, Bekenstein-hawking entropy and strange metals, Phys. Rev. X 5
2015
Earlier work this paper cites.
M. Blake, Universal charge diffusion and the butterfly effect in holographic theories, Phys. Rev. Lett. 117
2016
Earlier work this paper cites.
P. Hosur, X.-L. Qi, D. A. Roberts, and B. Yoshida, Chaos in quantum channels, J. High Energy Phys. 2016
Original
2016
Earlier work this paper cites.
J. Polchinski and V. Rosenhaus, The spectrum in the Sachdev-Ye-Kitaev model, J. High Energy Phys. 2016
Original
2016
Earlier work this paper cites.

Similar

J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94
Original
2016
Cited alongside, same era.
J. Maldacena, S. H. Shenker, and D. Stanford, A bound on chaos, J. High Energy Phys. 2016
2016
Cited alongside, same era.
W. Fu, D. Gaiotto, J. Maldacena, and S. Sachdev, Supersymmetric SYK models, Phys. Rev. D 95
Original
2016
Cited alongside, same era.
R. Gurau, The complete 1/N expansion of a SYK–like tensor model, Nucl. Phys. B 916
Original
2017
Cited alongside, same era.
Y. Gu, X.-L. Qi, and D. Stanford, Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models, J. High Energy Phys. 2017
2017
Cited alongside, same era.

Then

E. Witten, An SYK-like model without disorder, J. Phys. A Math. Theor. 52
2019
Later among the works it cites.
A. W. Harrow, L. Kong, Z.-W. Liu, S. Mehraban, and P. W. Shor, A separation of out-of-time-ordered correlator and entanglement, arXiv:1906.02219 (2019)
Original
2019
Later among the works it cites.
C.-F. Chen and A. Lucas, Operator growth bounds from graph theory, arXiv:1905.03682 (2019)
Original
2019
Later among the works it cites.
A. R. Brown, H. Gharibyan, S. Leichenauer, H. W. Lin, S. Nezami, G. Salton, L. Susskind, B. Swingle, and M. Walter, Quantum gravity in the lab: Teleportation by size and traversable wormholes, arXiv:1911.06314 (2019)
Original
2019
Later among the works it cites.
R. Babbush, D. W. Berry, and H. Neven, Quantum simulation of the Sachdev-Ye-Kitaev model by asymmetric qubitization, Phys. Rev. A 99

Beyond the bibliography

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I. Danshita, M. Hanada, and M. Tezuka, Creating and probing the Sachdev–Ye–Kitaev model with ultracold gases: Towards experimental studies of quantum gravity, Prog. Theor. Exp. Phys. 2017

2017

Cited alongside, same era.

D. I. Pikulin and M. Franz, Black hole on a chip: Proposal for a physical realization of the sachdev-ye-kitaev model in a solid-state system, Phys. Rev. X 7

2017

Cited alongside, same era.

L. García-Álvarez, I. L. Egusquiza, L. Lamata, A. del Campo, J. Sonner, and E. Solano, Digital quantum simulation of minimal AdS / CFT \mathrm{AdS}/\mathrm{CFT} , Phys. Rev. Lett. 119

2017

Cited alongside, same era.

J. Murugan, D. Stanford, and E. Witten, More on Supersymmetric and 2d Analogs of the SYK Model, J. High Energy Phys. 2017

Original

2017

Cited alongside, same era.

G. H. Low and I. L. Chuang, Optimal Hamiltonian Simulation by Quantum Signal Processing, Phys. Rev. Lett. 118

2017

Cited alongside, same era.

A. Lubotzky, High dimensional expanders, in Proc. Int. Congr. Math. ICM 2018 , Vol. 1 (2018) pp. 705–730, 1712.02526

Original

2018

Cited alongside, same era.

G. Brito, I. Dumitriu, and K. D. Harris, Spectral gap in random bipartite biregular graphs and applications, arXiv:1804.07808 (2018)

Original

2018

Cited alongside, same era.

2019