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

García-García, Antonio M.; Jia, Yiyang; Verbaarschot, Jacobus J. M.

doi:10.1103/PhysRevD.97.106003

Title: Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model

Abstract

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 $O(N)$ eigenvalues, the average spectral density is universal and well described by random matrix ensembles with chiral and superconducting discrete symmetries. The dynamics for $$E{\approx}0$$ is investigated by level fluctuations. Also in this case we find excellent agreement with the prediction of chiral and superconducting random matrix ensembles for eigenvalue separations smaller than the Thouless energy, which seems to scale linearly with $$N$$. Deviations beyond the Thouless energy, which describes how ergodicity is approached, are universally characterized by a quadratic growth of the number variance. In the time domain, we have found analytically that the spectral form factor $g(t)$, obtained from the connected two-level correlation function of the unfolded spectrum, decays as $$1/{t}^{2}$$ for times shorter but comparable to the Thouless time with $g(0)$ related to the coefficient of the quadratic growth of the number variance. Our results provide further support that quantum black holes are ergodic and therefore can be classified by random matrix theory.

Authors:: García-García, Antonio M.; Jia, Yiyang; Verbaarschot, Jacobus J. M.

Publication Date:: Fri May 04 00:00:00 EDT 2018

Research Org.:: Stony Brook Univ., NY (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP)

OSTI Identifier:: 1436006

Alternate Identifier(s):: OSTI ID: 1505151

Grant/Contract Number:: FG02-88ER40388

Resource Type:: Published Article

Journal Name:: Physical Review. D.

Additional Journal Information:: Journal Name: Physical Review. D. Journal Volume: 97 Journal Issue: 10; 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; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; quantum chaos; random matrix theory; string theory techniques in condensed matter

Citation Formats


                    García-García, Antonio M., Jia, Yiyang, and Verbaarschot, Jacobus J. M. Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model.  United States: N. p., 2018. 
Web.  doi:10.1103/PhysRevD.97.106003.

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                    García-García, Antonio M., Jia, Yiyang, & Verbaarschot, Jacobus J. M. Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model.  United States.  https://doi.org/10.1103/PhysRevD.97.106003

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                    García-García, Antonio M., Jia, Yiyang, and Verbaarschot, Jacobus J. M. Fri .  
"Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model".  United States.  https://doi.org/10.1103/PhysRevD.97.106003.

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@article{osti_1436006,

  title        = {Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model},

  author       = {García-García, Antonio M. and Jia, Yiyang and Verbaarschot, Jacobus J. M.},

  abstractNote = {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 $O(N)$ eigenvalues, the average spectral density is universal and well described by random matrix ensembles with chiral and superconducting discrete symmetries. The dynamics for $E{\approx}0$ is investigated by level fluctuations. Also in this case we find excellent agreement with the prediction of chiral and superconducting random matrix ensembles for eigenvalue separations smaller than the Thouless energy, which seems to scale linearly with $N$. Deviations beyond the Thouless energy, which describes how ergodicity is approached, are universally characterized by a quadratic growth of the number variance. In the time domain, we have found analytically that the spectral form factor $g(t)$, obtained from the connected two-level correlation function of the unfolded spectrum, decays as $1/{t}^{2}$ for times shorter but comparable to the Thouless time with $g(0)$ related to the coefficient of the quadratic growth of the number variance. Our results provide further support that quantum black holes are ergodic and therefore can be classified by random matrix theory.},

  doi          = {10.1103/PhysRevD.97.106003},

  journal      = {Physical Review. D.},

  number       = 10,

  volume       = 97,

  place        = {United States},

  year         = {Fri May 04 00:00:00 EDT 2018},

  month        = {Fri May 04 00:00:00 EDT 2018}

}

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Title: Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model

Abstract

Citation Formats

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Power-law decay exponents: A dynamical criterion for predicting thermalization journal, January 2017

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

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

Solvable Sachdev-Ye-Kitaev Models in Higher Dimensions: From Diffusion to Many-Body Localization journal, November 2017

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

A Class of Matrix Ensembles journal, January 1972

Chiral symmetry breaking in confining theories journal, June 1980

The supersymmetric technique for random-matrix ensembles with zero eigenvalues journal, January 2002

Quantum chaos and thermalization in isolated systems of interacting particles journal, April 2016

Generic dynamical features of quenched interacting quantum systems: Survival probability, density imbalance, and out-of-time-ordered correlator journal, February 2018

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

Phase Transition in the Density of States of Quantum Spin Glasses journal, December 2014

Contrasting SYK-like models journal, January 2018

Lower dimensional gravity journal, January 1985

A bound on chaos journal, August 2016

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

Complete random matrix classification of SYK models with N $$ \mathcal{N} $$ = 0, 1 and 2 supersymmetry journal, September 2017

Supersymmetric Sachdev-Ye-Kitaev models journal, January 2017

A Brownian‐Motion Model for the Eigenvalues of a Random Matrix journal, November 1962

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

The Combinatorics of q-Hermite polynomials and the Askey—Wilson Integral journal, October 1987

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

Holographic Metals and the Fractionalized Fermi Liquid journal, October 2010

Models of AdS2 backreaction and holography journal, November 2015

A supersymmetric SYK-like tensor model journal, May 2017

Quantum ergodicity in the SYK model journal, May 2018

Towards a 2d QFT analog of the SYK model journal, October 2017

Statistical Theory of the Energy Levels of Complex Systems. I journal, January 1962

Statistical Theory of the Energy Levels of Complex Systems. II journal, January 1962

Statistical Theory of the Energy Levels of Complex Systems. III journal, January 1962

Correlators in the N = 2 $$ \mathcal{N}=2 $$ supersymmetric SYK model journal, October 2017

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

Thouless Energy and Correlations of QCD Dirac Eigenvalues
journal, July 1998

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

Power-law decay exponents: A dynamical criterion for predicting thermalization
journal, January 2017

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

Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures
journal, January 1997

Supersymmetric SYK model and random matrix theory
journal, June 2017

Thermoelectric transport in disordered metals without quasiparticles: The Sachdev-Ye-Kitaev models and holography
journal, April 2017

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

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

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

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

Spectrum of the QCD Dirac operator and chiral random matrix theory
journal, April 1994

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

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

Quantum fluctuations of a nearly critical Heisenberg spin glass
journal, March 2001

Three dimensional view of the SYK/AdS duality
journal, September 2017

More on supersymmetric and 2d analogs of the SYK model
journal, August 2017

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

Random matrices and holographic tensor models
journal, June 2017

Publisher’s Note: Supersymmetric Sachdev-Ye-Kitaev models [Phys. Rev. D 95 , 026009 (2017)]
journal, March 2017

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

Spectral autocorrelation function in the statistical theory of energy levels
journal, October 1992

Asymptotic correlations at the spectrum edge of random matrices
journal, February 1995

Quasiparticle Lifetime in a Finite System: A Nonperturbative Approach
journal, April 1997

Uncolored random tensors, melon diagrams, and the Sachdev-Ye-Kitaev models
journal, February 2017

Conformal symmetry and its breaking in two-dimensional nearly anti-de Sitter space
journal, November 2016

Semiclassical analysis of spectral correlations in mesoscopic systems
journal, February 1993

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

Overscreened multichannel $SU (N)$ Kondo model: Large- $N$ solution and conformal field theory
journal, August 1998

Strongly Correlated Metal Built from Sachdev-Ye-Kitaev Models
journal, November 2017

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

Black holes and random matrices
journal, May 2017

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

Solvable Sachdev-Ye-Kitaev Models in Higher Dimensions: From Diffusion to Many-Body Localization
journal, November 2017

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

A Class of Matrix Ensembles
journal, January 1972

Chiral symmetry breaking in confining theories
journal, June 1980

The supersymmetric technique for random-matrix ensembles with zero eigenvalues
journal, January 2002

Quantum chaos and thermalization in isolated systems of interacting particles
journal, April 2016

Generic dynamical features of quenched interacting quantum systems: Survival probability, density imbalance, and out-of-time-ordered correlator
journal, February 2018

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

Phase Transition in the Density of States of Quantum Spin Glasses
journal, December 2014

Contrasting SYK-like models
journal, January 2018

Lower dimensional gravity
journal, January 1985

A bound on chaos
journal, August 2016

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

Complete random matrix classification of SYK models with N $$ \mathcal{N} $$ = 0, 1 and 2 supersymmetry
journal, September 2017

Supersymmetric Sachdev-Ye-Kitaev models
journal, January 2017

A Brownian‐Motion Model for the Eigenvalues of a Random Matrix
journal, November 1962

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

The Combinatorics of q-Hermite polynomials and the Askey—Wilson Integral
journal, October 1987

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

Holographic Metals and the Fractionalized Fermi Liquid
journal, October 2010

Models of AdS2 backreaction and holography
journal, November 2015

A supersymmetric SYK-like tensor model
journal, May 2017

Quantum ergodicity in the SYK model
journal, May 2018

Towards a 2d QFT analog of the SYK model
journal, October 2017

Statistical Theory of the Energy Levels of Complex Systems. I
journal, January 1962

Statistical Theory of the Energy Levels of Complex Systems. II
journal, January 1962

Statistical Theory of the Energy Levels of Complex Systems. III
journal, January 1962

Correlators in the N = 2 $$ \mathcal{N}=2 $$ supersymmetric SYK model
journal, October 2017

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