On the replica structure of Sachdev-Ye-Kitaev model
Abstract
We investigate existence of replica off-diagonal solutions in the field-theoretical description of Sachdev-Ye-Kitaev model. To this end we evaluate a set of local and non-local dynamic correlation functions in the long time limit. We argue that the structure of the soft-mode Schwarzian action is qualitatively different in replica-diagonal vs. replica-off-diagonal scenarios, leading to distinct long-time predictions for the correlation functions. We then evaluate the corresponding correlation functions numerically and compare the simulations with analytical predictions of replica-diagonal and replica-off-diagonal calculations. We conclude that all our numerical results are in a quantitative agreement with the theory based on the replica-diagonal saddle point plus Schwarzian and massive Gaussian fluctuations (the latter do contain replica off-diagonal components). This seems to exclude any contributions from replica-off-diagonal saddle points, at least on the time scales shorter than the inverse many-body level spacing.
- Authors:
-
[3];
- Univ. of Minnesota, Minneapolis, MN (United States)
- Universität zu Köln (Germany)
- Univ. of Hamburg (Germany)
- Publication Date:
- Research Org.:
- Yale Univ., New Haven, CT (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC); National Science Foundation (NSF)
- OSTI Identifier:
- 1609975
- Grant/Contract Number:
- FG02-08ER46482; DMR-1608238
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2019; Journal Issue: 9; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Berlin
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Random Systems; Field Theories in Lower Dimensions; Holography and condensed matter physics (AdS/CMT)
Citation Formats
Wang, Hanteng, Bagrets, D., Chudnovskiy, A. L., and Kamenev, A. On the replica structure of Sachdev-Ye-Kitaev model. United States: N. p., 2019.
Web. doi:10.1007/jhep09(2019)057.
Wang, Hanteng, Bagrets, D., Chudnovskiy, A. L., & Kamenev, A. On the replica structure of Sachdev-Ye-Kitaev model. United States. https://doi.org/10.1007/jhep09(2019)057
Wang, Hanteng, Bagrets, D., Chudnovskiy, A. L., and Kamenev, A. Mon .
"On the replica structure of Sachdev-Ye-Kitaev model". United States. https://doi.org/10.1007/jhep09(2019)057. https://www.osti.gov/servlets/purl/1609975.
@article{osti_1609975,
title = {On the replica structure of Sachdev-Ye-Kitaev model},
author = {Wang, Hanteng and Bagrets, D. and Chudnovskiy, A. L. and Kamenev, A.},
abstractNote = {We investigate existence of replica off-diagonal solutions in the field-theoretical description of Sachdev-Ye-Kitaev model. To this end we evaluate a set of local and non-local dynamic correlation functions in the long time limit. We argue that the structure of the soft-mode Schwarzian action is qualitatively different in replica-diagonal vs. replica-off-diagonal scenarios, leading to distinct long-time predictions for the correlation functions. We then evaluate the corresponding correlation functions numerically and compare the simulations with analytical predictions of replica-diagonal and replica-off-diagonal calculations. We conclude that all our numerical results are in a quantitative agreement with the theory based on the replica-diagonal saddle point plus Schwarzian and massive Gaussian fluctuations (the latter do contain replica off-diagonal components). This seems to exclude any contributions from replica-off-diagonal saddle points, at least on the time scales shorter than the inverse many-body level spacing.},
doi = {10.1007/jhep09(2019)057},
journal = {Journal of High Energy Physics (Online)},
number = 9,
volume = 2019,
place = {United States},
year = {Mon Sep 09 00:00:00 EDT 2019},
month = {Mon Sep 09 00:00:00 EDT 2019}
}
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Works referenced in this record:
Sachdev-Ye-Kitaev Model with Quadratic Perturbations: The Route to a Non-Fermi Liquid
journal, December 2018
- Lunkin, A. V.; Tikhonov, K. S.; Feigel’man, M. V.
- Physical Review Letters, Vol. 121, Issue 23
Sachdev–Ye–Kitaev model as Liouville quantum mechanics
journal, October 2016
- Bagrets, Dmitry; Altland, Alexander; Kamenev, Alex
- Nuclear Physics B, Vol. 911
Solving the Schwarzian via the conformal bootstrap
journal, August 2017
- Mertens, Thomas G.; Turiaci, Gustavo J.; Verlinde, Herman L.
- Journal of High Energy Physics, Vol. 2017, Issue 8
Power-law out of time order correlation functions in the SYK model
journal, August 2017
- Bagrets, Dmitry; Altland, Alexander; Kamenev, Alex
- Nuclear Physics B, Vol. 921
A bound on chaos
journal, August 2016
- Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas
- Journal of High Energy Physics, Vol. 2016, Issue 8
The Schwarzian theory — origins
journal, May 2018
- Mertens, Thomas G.
- Journal of High Energy Physics, Vol. 2018, Issue 5
Nonergodic Phases in Strongly Disordered Random Regular Graphs
journal, October 2016
- Altshuler, B. L.; Cuevas, E.; Ioffe, L. B.
- Physical Review Letters, Vol. 117, Issue 15
Higher dimensional generalizations of the SYK model
journal, January 2017
- Berkooz, Micha; Narayan, Prithvi; Rozali, Moshe
- Journal of High Energy Physics, Vol. 2017, Issue 1
Bi-local holography in the SYK model: perturbations
journal, November 2016
- Jevicki, Antal; Suzuki, Kenta
- Journal of High Energy Physics, Vol. 2016, Issue 11
Chaos in Holography
journal, September 2016
- Jensen, Kristan
- Physical Review Letters, Vol. 117, Issue 11
The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
journal, May 2018
- Kitaev, Alexei; Suh, S. Josephine
- Journal of High Energy Physics, Vol. 2018, Issue 5
Supersymmetric SYK model and random matrix theory
journal, June 2017
- Li, Tianlin; Liu, Junyu; Xin, Yuan
- Journal of High Energy Physics, Vol. 2017, Issue 6
The spectrum in the Sachdev-Ye-Kitaev model
journal, April 2016
- Polchinski, Joseph; Rosenhaus, Vladimir
- Journal of High Energy Physics, Vol. 2016, Issue 4
Chaos, complexity, and random matrices
journal, November 2017
- Cotler, Jordan; Hunter-Jones, Nicholas; Liu, Junyu
- Journal of High Energy Physics, Vol. 2017, Issue 11
Competition between Chaotic and Nonchaotic Phases in a Quadratically Coupled Sachdev-Ye-Kitaev Model
journal, November 2017
- Chen, Xin; Fan, Ruihua; Chen, Yiming
- Physical Review Letters, Vol. 119, Issue 20
Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
journal, May 2017
- Gu, Yingfei; Qi, Xiao-Liang; Stanford, Douglas
- Journal of High Energy Physics, Vol. 2017, Issue 5
Solvable Model of a Spin-Glass
journal, December 1975
- Sherrington, David; Kirkpatrick, Scott
- Physical Review Letters, Vol. 35, Issue 26
Level correlations in disordered metals: The replica model
journal, August 1999
- Kamenev, Alex; Mézard, Marc
- Physical Review B, Vol. 60, Issue 6
A supersymmetric SYK-like tensor model
journal, May 2017
- Peng, Cheng; Spradlin, Marcus; Volovich, Anastasia
- Journal of High Energy Physics, Vol. 2017, Issue 5
Energy diffusion and the butterfly effect in inhomogeneous Sachdev-Ye-Kitaev chains
journal, January 2017
- Gu, Yingfei; Lucas, Andrew; Qi, Xiao-Liang
- SciPost Physics, Vol. 2, Issue 3
Order Parameter for Spin-Glasses
journal, June 1983
- Parisi, Giorgio
- Physical Review Letters, Vol. 50, Issue 24
The Thouless time for mass-deformed SYK
journal, September 2018
- Nosaka, Tomoki; Rosa, Dario; Yoon, Junggi
- Journal of High Energy Physics, Vol. 2018, Issue 9
Quantum chaos and holographic tensor models
journal, March 2017
- Krishnan, Chethan; Sanyal, Sambuddha; Subramanian, P. N. Bala
- Journal of High Energy Physics, Vol. 2017, Issue 3
Replica-nondiagonal solutions in the SYK model
journal, July 2019
- Aref’eva, Irina; Khramtsov, Mikhail; Tikhanovskaya, Maria
- Journal of High Energy Physics, Vol. 2019, Issue 7
Quantum ergodicity in the SYK model
journal, May 2018
- Altland, Alexander; Bagrets, Dmitry
- Nuclear Physics B, Vol. 930
Does the SYK model have a spin glass phase?
journal, November 2018
- Gur-Ari, Guy; Mahajan, Raghu; Vaezi, Abolhassan
- Journal of High Energy Physics, Vol. 2018, Issue 11
Fermionic localization of the schwarzian theory
journal, October 2017
- Stanford, Douglas; Witten, Edward
- Journal of High Energy Physics, Vol. 2017, Issue 10
A generalization of Sachdev-Ye-Kitaev
journal, February 2017
- Gross, David J.; Rosenhaus, Vladimir
- Journal of High Energy Physics, Vol. 2017, Issue 2
Gapless spin-fluid ground state in a random quantum Heisenberg magnet
journal, May 1993
- Sachdev, Subir; Ye, Jinwu
- Physical Review Letters, Vol. 70, Issue 21
Models of AdS2 backreaction and holography
journal, November 2015
- Almheiri, Ahmed; Polchinski, Joseph
- Journal of High Energy Physics, Vol. 2015, Issue 11
An investigation of AdS2 backreaction and holography
journal, July 2016
- Engelsöy, Julius; Mertens, Thomas G.; Verlinde, Herman
- Journal of High Energy Physics, Vol. 2016, Issue 7
The bulk dual of SYK: cubic couplings
journal, May 2017
- Gross, David J.; Rosenhaus, Vladimir
- Journal of High Energy Physics, Vol. 2017, Issue 5
Bekenstein-Hawking Entropy and Strange Metals
journal, November 2015
- Sachdev, Subir
- Physical Review X, Vol. 5, Issue 4
Sachdev-Ye-Kitaev model and thermalization on the boundary of many-body localized fermionic symmetry-protected topological states
journal, March 2017
- You, Yi-Zhuang; Ludwig, Andreas W. W.; Xu, Cenke
- Physical Review B, Vol. 95, Issue 11
Disorder in the Sachdev–Ye–Kitaev model
journal, October 2017
- Liu, Yizhuang; Nowak, Maciej A.; Zahed, Ismail
- Physics Letters B, Vol. 773
Quantum quench of the Sachdev-Ye-Kitaev model
journal, November 2017
- Eberlein, Andreas; Kasper, Valentin; Sachdev, Subir
- Physical Review B, Vol. 96, Issue 20
Onset of random matrix behavior in scrambling systems
journal, July 2018
- Gharibyan, Hrant; Hanada, Masanori; Shenker, Stephen H.
- Journal of High Energy Physics, Vol. 2018, Issue 7
Solvable model for a dynamical quantum phase transition from fast to slow scrambling
journal, April 2017
- Banerjee, Sumilan; Altman, Ehud
- Physical Review B, Vol. 95, Issue 13
Strongly Correlated Metal Built from Sachdev-Ye-Kitaev Models
journal, November 2017
- Song, Xue-Yang; Jian, Chao-Ming; Balents, Leon
- Physical Review Letters, Vol. 119, Issue 21
Thermoelectric transport in disordered metals without quasiparticles: The Sachdev-Ye-Kitaev models and holography
journal, April 2017
- Davison, Richard A.; Fu, Wenbo; Georges, Antoine
- Physical Review B, Vol. 95, Issue 15
Instability of the non-Fermi-liquid state of the Sachdev-Ye-Kitaev model
journal, May 2017
- Bi, Zhen; Jian, Chao-Ming; You, Yi-Zhuang
- Physical Review B, Vol. 95, Issue 20
Topological Sachdev-Ye-Kitaev model
journal, May 2018
- Zhang, Pengfei; Zhai, Hui
- Physical Review B, Vol. 97, Issue 20
Supersymmetric Sachdev-Ye-Kitaev models
journal, January 2017
- Fu, Wenbo; Gaiotto, Davide; Maldacena, Juan
- Physical Review D, Vol. 95, Issue 2
The complete 1/N expansion of a SYK–like tensor model
journal, March 2017
- Gurau, Razvan
- Nuclear Physics B, Vol. 916
Uncolored random tensors, melon diagrams, and the Sachdev-Ye-Kitaev models
journal, February 2017
- Klebanov, Igor R.; Tarnopolsky, Grigory
- Physical Review D, Vol. 95, Issue 4
Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model
journal, June 2018
- García-García, Antonio M.; Loureiro, Bruno; Romero-Bermúdez, Aurelio
- Physical Review Letters, Vol. 120, Issue 24
Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
journal, December 2016
- García-García, Antonio M.; Verbaarschot, Jacobus J. M.
- Physical Review D, Vol. 94, Issue 12
Numerical study of fermion and boson models with infinite-range random interactions
journal, July 2016
- Fu, Wenbo; Sachdev, Subir
- Physical Review B, Vol. 94, Issue 3
The Schwarzian theory — a Wilson line perspective
journal, December 2018
- Blommaert, Andreas; Mertens, Thomas G.; Verschelde, Henri
- Journal of High Energy Physics, Vol. 2018, Issue 12
Theory of spin glasses
journal, May 1975
- Edwards, S. F.; Anderson, P. W.
- Journal of Physics F: Metal Physics, Vol. 5, Issue 5
Spin Glass Theory and Beyond: An Introduction to the Replica Method and Its Applications
book, November 1986
- Mezard, M.; Parisi, G.; Virasoro, M.
- World Scientific Lecture Notes in Physics
Quantum fluctuations of a nearly critical Heisenberg spin glass
journal, March 2001
- Georges, A.; Parcollet, O.; Sachdev, S.
- Physical Review B, Vol. 63, Issue 13
Correlation functions in Schwarzian liquid
journal, March 2019
- Qi, Yong-Hui; Seo, Yunseok; Sin, Sang-Jin
- Physical Review D, Vol. 99, Issue 6
Wigner-Dyson statistics from the replica method
journal, January 1999
- Kamenev, Alex; Mézard, Marc
- Journal of Physics A: Mathematical and General, Vol. 32, Issue 24
Nonperturbative results for level correlations from the replica nonlinear model
journal, August 1999
- Yurkevich, Igor V.; Lerner, Igor V.
- Physical Review B, Vol. 60, Issue 6
Replica treatment of non-Hermitian disordered Hamiltonians
journal, May 2002
- Nishigaki, Shinsuke M.; Kamenev, Alex
- Journal of Physics A: Mathematical and General, Vol. 35, Issue 21
Replica Field Theories, Painlevé Transcendents, and Exact Correlation Functions
journal, December 2002
- Kanzieper, Eugene
- Physical Review Letters, Vol. 89, Issue 25
Spectral Statistics beyond Random Matrix Theory
journal, July 1995
- Andreev, A. V.; Altshuler, B. L.
- Physical Review Letters, Vol. 75, Issue 5
Remarks on the Sachdev-Ye-Kitaev model
journal, November 2016
- Maldacena, Juan; Stanford, Douglas
- Physical Review D, Vol. 94, Issue 10
Conformal symmetry and its breaking in two-dimensional nearly anti-de Sitter space
journal, November 2016
- Maldacena, Juan; Stanford, Douglas; Yang, Zhenbin
- Progress of Theoretical and Experimental Physics, Vol. 2016, Issue 12
Non-ergodic delocalized phase in Anderson model on Bethe lattice and regular graph
journal, February 2018
- Kravtsov, V. E.; Altshuler, B. L.; Ioffe, L. B.
- Annals of Physics, Vol. 389
Fractality of wave functions on a Cayley tree: Difference between tree and locally treelike graph without boundary
journal, November 2016
- Tikhonov, K. S.; Mirlin, A. D.
- Physical Review B, Vol. 94, Issue 18
Statistics of eigenstates near the localization transition on random regular graphs
journal, January 2019
- Tikhonov, K. S.; Mirlin, A. D.
- Physical Review B, Vol. 99, Issue 2
Quantum ergodicity in the SYK model
text, January 2017
- Altland, Alexander; Bagrets, Dmitry
- Unpublished
The Spectrum in the Sachdev-Ye-Kitaev Model
text, January 2016
- Polchinski, Joseph; Rosenhaus, Vladimir
- arXiv
Energy diffusion and the butterfly effect in inhomogeneous Sachdev-Ye-Kitaev chains
text, January 2017
- Gu, Yingfei; Lucas, Andrew; Qi, Xiao-Liang
- arXiv
Fermionic Localization of the Schwarzian Theory
text, January 2017
- Stanford, Douglas; Witten, Edward
- arXiv
Competition between Chaotic and Non-Chaotic Phases in a Quadratically Coupled Sachdev-Ye-Kitaev Model
text, January 2017
- Chen, Xin; Fan, Ruihua; Chen, Yiming
- arXiv
Eigenstate thermalization in the Sachdev-Ye-Kitaev model
text, January 2017
- Sonner, Julian; Vielma, Manuel
- arXiv
Replica-nondiagonal solutions in the SYK model
text, January 2018
- Aref'eva, Irina; Khramtsov, Mikhail; Tikhanovskaya, Maria
- arXiv
Eigenstate thermalization in the Sachdev-Ye-Kitaev model
journal, November 2017
- Sonner, Julian; Vielma, Manuel
- Journal of High Energy Physics, Vol. 2017, Issue 11
Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
text, January 2016
- García-García, Am; Verbaarschot, Jjm
- Apollo - University of Cambridge Repository
Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
text, January 2016
- Bagrets, Dmitry; Altland, Alexander; Kamenev, Alex
- arXiv
Bi-Local Holography in the SYK Model: Perturbations
preprint, January 2016
- Jevicki, Antal; Suzuki, Kenta
- arXiv
Analytical Spectral Density of the Sachdev-Ye-Kitaev Model at finite N
text, January 2017
- García-García, Antonio M.; Verbaarschot, Jacobus J. M.
- arXiv
Solving the Schwarzian via the Conformal Bootstrap
text, January 2017
- Mertens, Thomas G.; Turiaci, Gustavo J.; Verlinde, Herman L.
- arXiv
Replica field theories, Painleve transcendents, and exact correlation functions
text, January 2002
- Kanzieper, Eugene
- arXiv
Non-perturbative results for level correlations from the replica nonlinear sigma model
text, January 1999
- Yurkevich, Igor V.; Lerner, Igor V.
- arXiv
Works referencing / citing this record:
Revealing Nonperturbative Effects in the SYK Model
journal, November 2019
- Aref’eva, I. Ya.; Volovich, I. V.; Khramtsov, M. A.
- Theoretical and Mathematical Physics, Vol. 201, Issue 2
Revealing nonperturbative effects in the SYK model
text, January 2019
- Aref'eva, Irina; Khramtsov, Mikhail; Volovich, Igor
- arXiv