Built on

D. Sherrington and S. Kirkpatrick, “Solvable Model of a Spin-Glass,” Phys. Rev. Lett. 35
1975
Earlier work this paper cites.
J. L. van Hemmen and R. G. Palmer, “The replica method and a solvable spin glass model,” Journal of Physics A: Mathematical and General 12
1979
Earlier work this paper cites.
M. Mezard, G. Parisi and M. Virasoro, “Spin Glass Theory and beyond,” World Scientific, 1987
1987
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.
V. Balasubramanian and S. F. Ross, “Holographic particle detection,” Phys. Rev. D 61
2000
Earlier work this paper cites.
A. Georges, O. Parcollet and S. Sachdev, “Quantum fluctuations of a nearly critical Heisenberg spin glass,” Phys. Rev. B 63
2001
Earlier work this paper cites.
J. M. Maldacena, “Eternal black holes in anti-de Sitter,” JHEP 0304
2003
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A. Khrennikov, A. Radyna, “Eigenvalues and Invertibility of Parisi Matrices. Ultramentric Group Point of View”, Advanced Studies in Contemporary Mathematica, 8, 95-102 (2004)
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Earlier work this paper cites.
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A. Kitaev, talks at KITP in 2015: http://online.kitp.ucsb.edu/online/entangled15/kitaev/ , http://online.kitp.ucsb.edu/online/entangled15/kitaev2/
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Earlier work this paper cites.
S. Sachdev, “Bekenstein-Hawking Entropy and Strange Metals,” Phys. Rev. X 5
Original
2015
Earlier work this paper cites.

Similar

P. Caputa, J. Simón, A. S̃tikonas, T. Takayanagi and K. Watanabe, “Scrambling time from local perturbations of the eternal BTZ black hole,” JHEP 1508
Original
2015
Cited alongside, same era.
J. Maldacena and D. Stanford, “Remarks on the Sachdev-Ye-Kitaev model,” Phys. Rev. D 94
Original
2016
Cited alongside, same era.
J. Polchinski and V. Rosenhaus, “The Spectrum in the Sachdev-Ye-Kitaev Model,” JHEP 1604
Original
2016
Cited alongside, same era.
K. Jensen, “Chaos in AdS 2 Holography,” Phys. Rev. Lett. 117
Original
2016
Cited alongside, same era.
J. Maldacena, D. Stanford and Z. Yang, “Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space,” PTEP 2016

Then

I. Ya. Aref’eva, M. A. Khramtsov and M. D. Tikhanovskaya, “Improved image method for a holographic description of conical defects,” Theor. Math. Phys. 189
Original
2016
Later among the works it cites.
D. Stanford and E. Witten, “Fermionic Localization of the Schwarzian Theory,” JHEP 1710
Original
2017
Later among the works it cites.
D. J. Gross and V. Rosenhaus, “All point correlation functions in SYK,” JHEP 1712
Original
2017
Later among the works it cites.
Y. Gu, X. L. Qi and D. Stanford, “Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models,” JHEP 1705
Original
2017
Later among the works it cites.
J. S. Cotler et al
Original

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2018

Replica-nondiagonal solutions in the SYK model

Aref'eva, Irina, Khramtsov, Mikhail, Tikhanovskaya, Maria et al.

Understand

We study the SYK model in the large $N$ limit beyond the replica-diagonal approximation.

First we show that there are exact replica-nondiagonal solutions of the saddle point equations for $q=2$ for any finite replica number $M$.
In the interacting $q=4$ case we are able to construct the numerical solutions, which are in one-to-one correspondence to the analytic solutions of the quadratic model.
These solutions are singular in the $M \to 0$ limit in both quadratic and quartic interaction cases.

Built on

D. Sherrington and S. Kirkpatrick, “Solvable Model of a Spin-Glass,” Phys. Rev. Lett. 35
1975
Earlier work this paper cites.
J. L. van Hemmen and R. G. Palmer, “The replica method and a solvable spin glass model,” Journal of Physics A: Mathematical and General 12
1979
Earlier work this paper cites.
M. Mezard, G. Parisi and M. Virasoro, “Spin Glass Theory and beyond,” World Scientific, 1987
1987
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.
V. Balasubramanian and S. F. Ross, “Holographic particle detection,” Phys. Rev. D 61
2000
Earlier work this paper cites.
A. Georges, O. Parcollet and S. Sachdev, “Quantum fluctuations of a nearly critical Heisenberg spin glass,” Phys. Rev. B 63
2001
Earlier work this paper cites.
J. M. Maldacena, “Eternal black holes in anti-de Sitter,” JHEP 0304
2003
Earlier work this paper cites.
A. Khrennikov, A. Radyna, “Eigenvalues and Invertibility of Parisi Matrices. Ultramentric Group Point of View”, Advanced Studies in Contemporary Mathematica, 8, 95-102 (2004)
2004
Earlier work this paper cites.
C. De Dominicis, I. Giardina, “Random fields and spin glasses: a field theory approach,” Cambridge University Press, 2006
2006
Earlier work this paper cites.
A. Kitaev, talks at KITP in 2015: http://online.kitp.ucsb.edu/online/entangled15/kitaev/ , http://online.kitp.ucsb.edu/online/entangled15/kitaev2/
2015
Earlier work this paper cites.
S. Sachdev, “Bekenstein-Hawking Entropy and Strange Metals,” Phys. Rev. X 5
Original
2015
Earlier work this paper cites.

Similar

P. Caputa, J. Simón, A. S̃tikonas, T. Takayanagi and K. Watanabe, “Scrambling time from local perturbations of the eternal BTZ black hole,” JHEP 1508
Original
2015
Cited alongside, same era.
J. Maldacena and D. Stanford, “Remarks on the Sachdev-Ye-Kitaev model,” Phys. Rev. D 94
Original
2016
Cited alongside, same era.
J. Polchinski and V. Rosenhaus, “The Spectrum in the Sachdev-Ye-Kitaev Model,” JHEP 1604
Original
2016
Cited alongside, same era.
K. Jensen, “Chaos in AdS 2 Holography,” Phys. Rev. Lett. 117
Original
2016
Cited alongside, same era.
J. Maldacena, D. Stanford and Z. Yang, “Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space,” PTEP 2016

Then

I. Ya. Aref’eva, M. A. Khramtsov and M. D. Tikhanovskaya, “Improved image method for a holographic description of conical defects,” Theor. Math. Phys. 189
Original
2016
Later among the works it cites.
D. Stanford and E. Witten, “Fermionic Localization of the Schwarzian Theory,” JHEP 1710
Original
2017
Later among the works it cites.
D. J. Gross and V. Rosenhaus, “All point correlation functions in SYK,” JHEP 1712
Original
2017
Later among the works it cites.
Y. Gu, X. L. Qi and D. Stanford, “Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models,” JHEP 1705
Original
2017
Later among the works it cites.
J. S. Cotler et al
Original

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

2016

Cited alongside, same era.

J. Engelsöy, T. G. Mertens and H. Verlinde, “An investigation of AdS 2

Original

2016

Cited alongside, same era.

A. Jevicki, K. Suzuki and J. Yoon, “Bi-Local Holography in the SYK Model,” JHEP 1607

Original

2016

Cited alongside, same era.

D. Bagrets, A. Altland and A. Kamenev, “Sachdev–Ye–Kitaev model as Liouville quantum mechanics,” Nucl. Phys. B 911

Original

2016

Cited alongside, same era.

A. M. García-García and J. J. M. Verbaarschot, “Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model,” Phys. Rev. D 94

Original

2016

Cited alongside, same era.

W. Fu and S. Sachdev, “Numerical study of fermion and boson models with infinite-range random interactions,” Phys. Rev. B 94

Original

2016

Cited alongside, same era.

D. Anninos, T. Anous and F. Denef, “Disordered Quivers and Cold Horizons,” JHEP 1612

Original

2016

Cited alongside, same era.

A. Kitaev and S. J. Suh, “The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual,” arXiv:1711.08467 [hep-th]

Original

Cited in the paper.

2017

Later among the works it cites.

D. J. Gross and V. Rosenhaus, “A Generalization of Sachdev-Ye-Kitaev,” JHEP 1702

Original

2017

Later among the works it cites.

G. Sárosi, “AdS 2

Original

2018

Closest in time.

A. Kamenev, talk at Steklov Mathematical Institute, March 2018

2018

Closest in time.

I. Aref’eva and I. Volovich, “Notes on the SYK model in real time,” Theoret. and Math. Phys., 197:2 (2018), 1650-1662, DOI: https://doi.org/10.4213/tmf9533 [arXiv:1801.08118 [hep-th]]

Original

2018

Closest in time.

I. Ya. Aref’eva, M. A. Khramtsov, M. D. Tikhanovskaya and I. V. Volovich, ”On replica-nondiagonal large N saddles in the SYK model”, EPJ Web of Conferences 191, 06007 (2018); DOI: https://doi.org/10.1051/epjconf/201819106007

2018

Closest in time.