On the replica structure of Sachdev-Ye-Kitaev model

doi:https://doi.org/10.1007/jhep09(2019)057

Title: 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:

Wang, Hanteng ^[1]; Bagrets, D. ^[2];

^[3]; Kamenev, A. ^[1]

Univ. of Minnesota, Minneapolis, MN (United States)
Universität zu Köln (Germany)
Univ. of Hamburg (Germany)

Publication Date:: 2019-09-09

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:: Journal Article: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: 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.

Copy to clipboard


                    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

Copy to clipboard


                    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.

Copy to clipboard


                    
@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},

  url          = {https://www.osti.gov/biblio/1609975},
  journal      = {Journal of High Energy Physics (Online)},

  issn         = {1029-8479},

  number       = 9,

  volume       = 2019,

  place        = {United States},

  year         = {2019},

  month        = {9}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1007/jhep09(2019)057

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 4 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

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
https://doi.org/10.1103/PhysRevLett.121.236601

Sachdev–Ye–Kitaev model as Liouville quantum mechanics
journal, October 2016

Bagrets, Dmitry; Altland, Alexander; Kamenev, Alex
Nuclear Physics B, Vol. 911
https://doi.org/10.1016/j.nuclphysb.2016.08.002

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
https://doi.org/10.1007/JHEP08(2017)136

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
https://doi.org/10.1016/j.nuclphysb.2017.06.012

A bound on chaos
journal, August 2016

Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas
Journal of High Energy Physics, Vol. 2016, Issue 8
https://doi.org/10.1007/JHEP08(2016)106

The Schwarzian theory — origins
journal, May 2018

Mertens, Thomas G.
Journal of High Energy Physics, Vol. 2018, Issue 5
https://doi.org/10.1007/JHEP05(2018)036

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
https://doi.org/10.1103/PhysRevLett.117.156601

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
https://doi.org/10.1007/JHEP01(2017)138

Shockwave S-matrix from Schwarzian quantum mechanics
journal, November 2018

Lam, Ho Tat; Mertens, Thomas G.; Turiaci, Gustavo J.
Journal of High Energy Physics, Vol. 2018, Issue 11
https://doi.org/10.1007/JHEP11(2018)182

Bi-local holography in the SYK model: perturbations
journal, November 2016

Jevicki, Antal; Suzuki, Kenta
Journal of High Energy Physics, Vol. 2016, Issue 11
https://doi.org/10.1007/JHEP11(2016)046

Chaos in ${AdS}_{2}$ Holography
journal, September 2016

Jensen, Kristan
Physical Review Letters, Vol. 117, Issue 11
https://doi.org/10.1103/PhysRevLett.117.111601

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
https://doi.org/10.1007/JHEP05(2018)183

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
https://doi.org/10.1007/JHEP06(2017)111

Eigenstate thermalization in the Sachdev-Ye-Kitaev model
journal, November 2017

Sonner, Julian; Vielma, Manuel
Journal of High Energy Physics, Vol. 2017, Issue 11
https://doi.org/10.1007/JHEP11(2017)149

The spectrum in the Sachdev-Ye-Kitaev model
journal, April 2016

Polchinski, Joseph; Rosenhaus, Vladimir
Journal of High Energy Physics, Vol. 2016, Issue 4
https://doi.org/10.1007/JHEP04(2016)001

Chaos, complexity, and random matrices
journal, November 2017

Cotler, Jordan; Hunter-Jones, Nicholas; Liu, Junyu
Journal of High Energy Physics, Vol. 2017, Issue 11
https://doi.org/10.1007/JHEP11(2017)048

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
https://doi.org/10.1103/PhysRevLett.119.207603

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
https://doi.org/10.1007/JHEP05(2017)125

Solvable Model of a Spin-Glass
journal, December 1975

Sherrington, David; Kirkpatrick, Scott
Physical Review Letters, Vol. 35, Issue 26
https://doi.org/10.1103/PhysRevLett.35.1792

Level correlations in disordered metals: The replica $σ$ model
journal, August 1999

Kamenev, Alex; Mézard, Marc
Physical Review B, Vol. 60, Issue 6
https://doi.org/10.1103/PhysRevB.60.3944

A supersymmetric SYK-like tensor model
journal, May 2017

Peng, Cheng; Spradlin, Marcus; Volovich, Anastasia
Journal of High Energy Physics, Vol. 2017, Issue 5
https://doi.org/10.1007/JHEP05(2017)062

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
https://doi.org/10.21468/SciPostPhys.2.3.018

Order Parameter for Spin-Glasses
journal, June 1983

Parisi, Giorgio
Physical Review Letters, Vol. 50, Issue 24
https://doi.org/10.1103/PhysRevLett.50.1946

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
https://doi.org/10.1007/JHEP09(2018)041

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
https://doi.org/10.1007/JHEP03(2017)056

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
https://doi.org/10.1007/JHEP07(2019)113

Quantum ergodicity in the SYK model
journal, May 2018

Altland, Alexander; Bagrets, Dmitry
Nuclear Physics B, Vol. 930
https://doi.org/10.1016/j.nuclphysb.2018.02.015

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
https://doi.org/10.1007/JHEP11(2018)070

Fermionic localization of the schwarzian theory
journal, October 2017

Stanford, Douglas; Witten, Edward
Journal of High Energy Physics, Vol. 2017, Issue 10
https://doi.org/10.1007/JHEP10(2017)008

A generalization of Sachdev-Ye-Kitaev
journal, February 2017

Gross, David J.; Rosenhaus, Vladimir
Journal of High Energy Physics, Vol. 2017, Issue 2
https://doi.org/10.1007/JHEP02(2017)093

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
https://doi.org/10.1134/s0040577919110059

Similar records in OSTI.GOV collections:

Supersymmetric Sachdev-Ye-Kitaev models

Journal Article Fu, Wenbo ; Gaiotto, Davide ; Maldacena, Juan ; ... - Physical Review D

We discuss a supersymmetric generalization of the Sachdev-Ye-Kitaev (SYK) model. These are quantum mechanical models involving N Majorana fermions. The supercharge is given by a polynomial expression in terms of the Majorana fermions with random coefficients. The Hamiltonian is the square of the supercharge. The N = 1 model with a single supercharge has unbroken supersymmetry at large N , but nonperturbatively spontaneously broken supersymmetry in the exact theory. We analyze the model by looking at the large N equation, and also by performing numerical computations for small values of N . We also compute the large N spectrum ofmore »« less
Cited by 56
https://doi.org/10.1103/PhysRevD.95.026009

Full Text Available
Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model

Journal Article García-García, Antonio M. ; Jia, Yiyang ; Verbaarschot, Jacobus J. M. - Physical Review D

We investigate the supersymmetric Sachdev-Ye-Kitaev (SYK) model, $$N$$ Majorana fermions with infinite range interactions in $0+1$ dimensions. We have found that, close to the ground state $$E{\approx}0$$, discrete symmetries alter qualitatively the spectral properties with respect to the non-supersymmetric SYK model. The average spectral density at finite $$N$$, which we compute analytically and numerically, grows exponentially with $$N$$ for $$E{\approx}0$$. However the chiral condensate, which is normalized with respect the total number of eigenvalues, vanishes in the thermodynamic limit. Slightly above $$E{\approx}0$$, the spectral density grows exponentially with the energy. Deep in the quantum regime, corresponding to the first $O(N)$more »« less
Cited by 9
https://doi.org/10.1103/PhysRevD.97.106003
Sachdev–Ye–Kitaev model as Liouville quantum mechanics

Journal Article Bagrets, Dmitry ; Altland, Alexander ; Kamenev, Alex - Nuclear Physics. B

Here, we show that the proper inclusion of soft reparameterization modes in the Sachdev–Ye–Kitaev model of N randomly interacting Majorana fermions reduces its long-time behavior to that of Liouville quantum mechanics.
Cited by 30
https://doi.org/10.1016/j.nuclphysb.2016.08.002
Remarks on the Sachdev-Ye-Kitaev model

Journal Article Maldacena, Juan ; Stanford, Douglas - Physical Review D

We study a quantum mechanical model proposed by Sachdev, Ye and Kitaev. The model consists of N Majorana fermions with random interactions of a few fermions at a time. It it tractable in the large N limit, where the classical variable is a bilocal fermion bilinear. The model becomes strongly interacting at low energies where it develops an emergent conformal symmetry. We study two and four point functions of the fundamental fermions. This provides the spectrum of physical excitations for the bilocal field. The emergent conformal symmetry is a reparametrization symmetry, which is spontaneously broken to SL(2;R), leading to zeromore »« less
Cited by 125
https://doi.org/10.1103/physrevd.94.106002

Full Text Available
Linear resistivity and Sachdev-Ye-Kitaev (SYK) spin liquid behavior in a quantum critical metal with spin-1/2 fermions

Journal Article Cha, Peter ; Wentzell, Nils ; Parcollet, Olivier ; ... - Proceedings of the National Academy of Sciences of the United States of America

“Smore »« less
https://doi.org/10.1073/pnas.2003179117

Similar Records

Title: On the replica structure of Sachdev-Ye-Kitaev model

Abstract

Citation Formats

Sachdev-Ye-Kitaev Model with Quadratic Perturbations: The Route to a Non-Fermi Liquid journal, December 2018

Sachdev–Ye–Kitaev model as Liouville quantum mechanics journal, October 2016

Solving the Schwarzian via the conformal bootstrap journal, August 2017

Power-law out of time order correlation functions in the SYK model journal, August 2017

A bound on chaos journal, August 2016

The Schwarzian theory — origins journal, May 2018

Nonergodic Phases in Strongly Disordered Random Regular Graphs journal, October 2016

Higher dimensional generalizations of the SYK model journal, January 2017

Shockwave S-matrix from Schwarzian quantum mechanics journal, November 2018

Bi-local holography in the SYK model: perturbations journal, November 2016

Chaos in AdS 2 Holography journal, September 2016

The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual journal, May 2018

Supersymmetric SYK model and random matrix theory journal, June 2017

Eigenstate thermalization in the Sachdev-Ye-Kitaev model journal, November 2017

The spectrum in the Sachdev-Ye-Kitaev model journal, April 2016

Chaos, complexity, and random matrices journal, November 2017

Competition between Chaotic and Nonchaotic Phases in a Quadratically Coupled Sachdev-Ye-Kitaev Model journal, November 2017

Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models journal, May 2017

Solvable Model of a Spin-Glass journal, December 1975

Level correlations in disordered metals: The replica σ model journal, August 1999

A supersymmetric SYK-like tensor model journal, May 2017

Energy diffusion and the butterfly effect in inhomogeneous Sachdev-Ye-Kitaev chains journal, January 2017

Order Parameter for Spin-Glasses journal, June 1983

The Thouless time for mass-deformed SYK journal, September 2018

Quantum chaos and holographic tensor models journal, March 2017

Replica-nondiagonal solutions in the SYK model journal, July 2019

Quantum ergodicity in the SYK model journal, May 2018

Does the SYK model have a spin glass phase? journal, November 2018

Fermionic localization of the schwarzian theory journal, October 2017

A generalization of Sachdev-Ye-Kitaev journal, February 2017

Revealing Nonperturbative Effects in the SYK Model journal, November 2019

Sachdev-Ye-Kitaev Model with Quadratic Perturbations: The Route to a Non-Fermi Liquid
journal, December 2018

Sachdev–Ye–Kitaev model as Liouville quantum mechanics
journal, October 2016

Solving the Schwarzian via the conformal bootstrap
journal, August 2017

Power-law out of time order correlation functions in the SYK model
journal, August 2017

A bound on chaos
journal, August 2016

The Schwarzian theory — origins
journal, May 2018

Nonergodic Phases in Strongly Disordered Random Regular Graphs
journal, October 2016

Higher dimensional generalizations of the SYK model
journal, January 2017

Shockwave S-matrix from Schwarzian quantum mechanics
journal, November 2018

Bi-local holography in the SYK model: perturbations
journal, November 2016

Chaos in ${AdS}_{2}$ Holography
journal, September 2016

The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
journal, May 2018

Supersymmetric SYK model and random matrix theory
journal, June 2017

Eigenstate thermalization in the Sachdev-Ye-Kitaev model
journal, November 2017

The spectrum in the Sachdev-Ye-Kitaev model
journal, April 2016

Chaos, complexity, and random matrices
journal, November 2017

Competition between Chaotic and Nonchaotic Phases in a Quadratically Coupled Sachdev-Ye-Kitaev Model
journal, November 2017

Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
journal, May 2017

Solvable Model of a Spin-Glass
journal, December 1975

Level correlations in disordered metals: The replica $σ$ model
journal, August 1999

A supersymmetric SYK-like tensor model
journal, May 2017

Energy diffusion and the butterfly effect in inhomogeneous Sachdev-Ye-Kitaev chains
journal, January 2017

Order Parameter for Spin-Glasses
journal, June 1983

The Thouless time for mass-deformed SYK
journal, September 2018

Quantum chaos and holographic tensor models
journal, March 2017

Replica-nondiagonal solutions in the SYK model
journal, July 2019

Quantum ergodicity in the SYK model
journal, May 2018

Does the SYK model have a spin glass phase?
journal, November 2018

Fermionic localization of the schwarzian theory
journal, October 2017

A generalization of Sachdev-Ye-Kitaev
journal, February 2017

Revealing Nonperturbative Effects in the SYK Model
journal, November 2019