skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Quantum chaos transition in a two-site Sachdev-Ye-Kitaev model dual to an eternal traversable wormhole

Abstract

It has been recently proposed by Maldacena and Qi that an eternal traversable wormhole in a two-dimensional anti–de Sitter space is the gravity dual of the low temperature limit of two Sachdev-Ye-Kitaev (SYK) models coupled by a relevant interaction (which we will refer to as spin operator). We study spectral and eigenstate properties of this coupled SYK model. We find that level statistics in the tail of the spectrum, and for a sufficiently weak coupling, show substantial deviations from random matrix theory, which suggests that traversable wormholes are not quantum chaotic. By contrast, for sufficiently strong coupling, corresponding to the black hole phase, level statistics are well described by random matrix theory. This transition in level statistics coincides approximately with a previously reported Hawking-Page transition for weak coupling. We show explicitly that this thermodynamic transition turns into a sharp crossover as the coupling increases. Likewise, this critical coupling also corresponds to the one at which the overlap between the ground state and the thermofield double state (TFD) is smallest. In the range of sizes we can reach by exact diagonalization, the ground state is well approximated by the TFD only in the strong coupling limit. This is due to themore » fact that the ground state is close to the eigenstate of the spin operator corresponding to the lowest eigenvalue which is an exact TFD at infinite temperature. In this region, the spectral density is separated into blobs centered around the eigenvalues of the spin operator. For weaker couplings, the exponential decay of coefficients in a tensor product basis, typical of the TFD, becomes power law. Finally, we also find that the total Hamiltonian has an additional discrete symmetry which has not been reported previously.« less

Authors:
; ; ;
Publication Date:
Research Org.:
State Univ. of New York (SUNY), Albany, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC); National Science Foundation (NSF)
OSTI Identifier:
1532437
Alternate Identifier(s):
OSTI ID: 1610129
Grant/Contract Number:  
FG02-88ER40388; PHY-1607611
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 2; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; astronomy & astrophysics; physics; gauge-gravity dualities; quantum aspects of black holes; quantum chaos; quantum gravity; random matrix theory

Citation Formats

García-García, Antonio M., Nosaka, Tomoki, Rosa, Dario, and Verbaarschot, Jacobus J. M. Quantum chaos transition in a two-site Sachdev-Ye-Kitaev model dual to an eternal traversable wormhole. United States: N. p., 2019. Web. doi:10.1103/PhysRevD.100.026002.
García-García, Antonio M., Nosaka, Tomoki, Rosa, Dario, & Verbaarschot, Jacobus J. M. Quantum chaos transition in a two-site Sachdev-Ye-Kitaev model dual to an eternal traversable wormhole. United States. doi:10.1103/PhysRevD.100.026002.
García-García, Antonio M., Nosaka, Tomoki, Rosa, Dario, and Verbaarschot, Jacobus J. M. Mon . "Quantum chaos transition in a two-site Sachdev-Ye-Kitaev model dual to an eternal traversable wormhole". United States. doi:10.1103/PhysRevD.100.026002.
@article{osti_1532437,
title = {Quantum chaos transition in a two-site Sachdev-Ye-Kitaev model dual to an eternal traversable wormhole},
author = {García-García, Antonio M. and Nosaka, Tomoki and Rosa, Dario and Verbaarschot, Jacobus J. M.},
abstractNote = {It has been recently proposed by Maldacena and Qi that an eternal traversable wormhole in a two-dimensional anti–de Sitter space is the gravity dual of the low temperature limit of two Sachdev-Ye-Kitaev (SYK) models coupled by a relevant interaction (which we will refer to as spin operator). We study spectral and eigenstate properties of this coupled SYK model. We find that level statistics in the tail of the spectrum, and for a sufficiently weak coupling, show substantial deviations from random matrix theory, which suggests that traversable wormholes are not quantum chaotic. By contrast, for sufficiently strong coupling, corresponding to the black hole phase, level statistics are well described by random matrix theory. This transition in level statistics coincides approximately with a previously reported Hawking-Page transition for weak coupling. We show explicitly that this thermodynamic transition turns into a sharp crossover as the coupling increases. Likewise, this critical coupling also corresponds to the one at which the overlap between the ground state and the thermofield double state (TFD) is smallest. In the range of sizes we can reach by exact diagonalization, the ground state is well approximated by the TFD only in the strong coupling limit. This is due to the fact that the ground state is close to the eigenstate of the spin operator corresponding to the lowest eigenvalue which is an exact TFD at infinite temperature. In this region, the spectral density is separated into blobs centered around the eigenvalues of the spin operator. For weaker couplings, the exponential decay of coefficients in a tensor product basis, typical of the TFD, becomes power law. Finally, we also find that the total Hamiltonian has an additional discrete symmetry which has not been reported previously.},
doi = {10.1103/PhysRevD.100.026002},
journal = {Physical Review D},
number = 2,
volume = 100,
place = {United States},
year = {2019},
month = {7}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevD.100.026002

Citation Metrics:
Cited by: 8 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

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
  • DOI: 10.1007/JHEP08(2017)136

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


Anomalous Thouless energy and critical statistics on the metallic side of the many-body localization transition
journal, October 2016


A perturbative perspective on self-supporting wormholes
journal, January 2019

  • Fu, Zicao; Grado-White, Brianna; Marolf, Donald
  • Classical and Quantum Gravity, Vol. 36, Issue 4
  • DOI: 10.1088/1361-6382/aafcea

Bulk view of teleportation and traversable wormholes
journal, August 2018

  • Bak, Dongsu; Kim, Chanju; Yi, Sang-Heon
  • Journal of High Energy Physics, Vol. 2018, Issue 8
  • DOI: 10.1007/JHEP08(2018)140

Phase Diagram of Planar Matrix Quantum Mechanics, Tensor, and Sachdev-Ye-Kitaev Models
journal, February 2018


Random-matrix theories in quantum physics: common concepts
journal, June 1998


Many-body localization edge in the random-field Heisenberg chain
journal, February 2015


Spacing and individual eigenvalue distributions of two-body random hamiltonians
journal, June 1971


Traversable wormholes via a double trace deformation
journal, December 2017

  • Gao, Ping; Jafferis, Daniel Louis; Wall, Aron C.
  • Journal of High Energy Physics, Vol. 2017, Issue 12
  • DOI: 10.1007/JHEP12(2017)151

How to build the thermofield double state
journal, February 2019

  • Cottrell, William; Freivogel, Ben; Hofman, Diego M.
  • Journal of High Energy Physics, Vol. 2019, Issue 2
  • DOI: 10.1007/JHEP02(2019)058

Spectral density of the QCD Dirac operator near zero virtuality
journal, June 1993


Gapless spin-fluid ground state in a random quantum Heisenberg magnet
journal, May 1993


Experimental Study of the BEC-BCS Crossover Region in Lithium 6
journal, July 2004


Random matrix theory and spectral sum rules for the Dirac operator in QCD
journal, July 1993


Statistical properties of many-particle spectra
journal, November 1975


Bi-local holography in the SYK model
journal, July 2016

  • Jevicki, Antal; Suzuki, Kenta; Yoon, Junggi
  • Journal of High Energy Physics, Vol. 2016, Issue 7
  • DOI: 10.1007/JHEP07(2016)007

Possible third-order phase transition in the large- N lattice gauge theory
journal, January 1980


Validity of random matrix theories for many-particle systems
journal, December 1970


Some random-matrix level and spacing distributions for fixed-particle-rank interactions
journal, April 1971


Review of the k -body embedded ensembles of Gaussian random matrices
journal, March 2003


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
  • DOI: 10.1007/JHEP11(2018)070

Traversable wormholes as quantum channels: exploring CFT entanglement structure and channel capacity in holography
journal, November 2018

  • Bao, Ning; Chatwin-Davies, Aidan; Pollack, Jason
  • Journal of High Energy Physics, Vol. 2018, Issue 11
  • DOI: 10.1007/JHEP11(2018)071

Distribution of the Ratio of Consecutive Level Spacings in Random Matrix Ensembles
journal, February 2013


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
  • DOI: 10.1093/ptep/ptw124

Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation Laws
journal, January 1984


On the statistical distribution of the widths and spacings of nuclear resonance levels
journal, October 1951

  • Wigner, Eugene P.
  • Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 47, Issue 4
  • DOI: 10.1017/S0305004100027237

Black holes and random matrices
journal, May 2017

  • Cotler, Jordan S.; Gur-Ari, Guy; Hanada, Masanori
  • Journal of High Energy Physics, Vol. 2017, Issue 5
  • DOI: 10.1007/JHEP05(2017)118

Analytical spectral density of the Sachdev-Ye-Kitaev model at finite N
journal, September 2017


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


Localization of interacting fermions at high temperature
journal, April 2007


Lower dimensional gravity
journal, January 1985


A bound on chaos
journal, August 2016

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

Supersymmetry and theory of disordered metals
journal, January 1983


Atomic vibrations in vitreous silica
journal, January 1970


Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
journal, December 2016


Supersymmetric Sachdev-Ye-Kitaev models
journal, January 2017


A statistical study of shell-model eigenvectors
journal, November 1979


Remarks on the Sachdev-Ye-Kitaev model
journal, November 2016


Chaos in AdS 2 Holography
journal, September 2016


Gravitation and hamiltonian structure in two spacetime dimensions
journal, June 1983


Four-dimensional traversable wormholes and bouncing cosmologies in vacuum
journal, April 2019


Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model
journal, May 2018

  • García-García, Antonio M.; Jia, Yiyang; Verbaarschot, Jacobus J. M.
  • Physical Review D, Vol. 97, Issue 10
  • DOI: 10.1103/PhysRevD.97.106003

Nearly AdS2 sugra and the super-Schwarzian
journal, August 2017


Diving into traversable wormholes: Diving into traversable wormholes
journal, May 2017

  • Maldacena, Juan; Stanford, Douglas; Yang, Zhenbin
  • Fortschritte der Physik, Vol. 65, Issue 5
  • DOI: 10.1002/prop.201700034

Holographic Metals and the Fractionalized Fermi Liquid
journal, October 2010


Models of AdS2 backreaction and holography
journal, November 2015

  • Almheiri, Ahmed; Polchinski, Joseph
  • Journal of High Energy Physics, Vol. 2015, Issue 11
  • DOI: 10.1007/JHEP11(2015)014

Quantum ergodicity in the SYK model
journal, May 2018


Fermionic localization of the schwarzian theory
journal, October 2017

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

Exact solution of the Schwarzian theory
journal, November 2017


Two-body random hamiltonian and level density
journal, March 1971