Sparse Sachdev-Ye-Kitaev model, quantum chaos, and gravity duals

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

doi:10.1103/PhysRevD.103.106002

Title: Sparse Sachdev-Ye-Kitaev model, quantum chaos, and gravity duals

Abstract

We study a sparse Sachdev-Ye-Kitaev (SYK) model with N Majoranas where only ~ kN independent matrix elements are nonzero. We identify a minimum k ≳ 1 for quantum chaos to occur by a level statistics analysis. The spectral density in this region, and for a larger k, is still given by the Schwarzian prediction of the dense SYK model, though with renormalized parameters. Similar results are obtained for a beyond linear scaling with N of the number of nonzero matrix elements. This is a strong indication that this is the minimum connectivity for the sparse SYK model to still have a quantum gravity dual. We also find an intriguing exact relation between the leading correction to moments of the spectral density due to sparsity and the leading 1/d correction of Parisi’s U(1) lattice gauge theory in a d -dimensional hypercube. In the k → 1 limit, different disorder realizations of the sparse SYK model show emergent random matrix statistics that for fixed N can be in any universality class of the tenfold way. The agreement with random matrix statistics is restricted to short-range correlations, no more than a few level spacings, in particular in the tail of the spectrum. Inmore »« less

Authors:

García-García, Antonio M.;

; Rosa, Dario; Verbaarschot, Jacobus J. M.

Publication Date:: Mon May 03 00:00:00 EDT 2021

Research Org.:: State Univ. of New York (SUNY), Albany, NY (United States); Stony Brook Univ., NY (United States)

Sponsoring Org.:: USDOE Office of Science (SC); National Natural Science Foundation of China (NSFC); Korea Institute of Advanced Study (KIAS)

OSTI Identifier:: 1781178

Alternate Identifier(s):: OSTI ID: 1849986; OSTI ID: 2280817

Grant/Contract Number:: FAG-88FR40388; FG02-88ER40388; 11874259; PG059602

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 103 Journal Issue: 10; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Astronomy & Astrophysics; Physics; Sachdev-Ye-Kitaev model; Lattice models in condensed matter; Field and string theory models and techniques; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats


                    García-García, Antonio M., Jia, Yiyang, Rosa, Dario, and Verbaarschot, Jacobus J. M. Sparse Sachdev-Ye-Kitaev model, quantum chaos, and gravity duals.  United States: N. p., 2021. 
Web.  doi:10.1103/PhysRevD.103.106002.

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                    García-García, Antonio M., Jia, Yiyang, Rosa, Dario, & Verbaarschot, Jacobus J. M. Sparse Sachdev-Ye-Kitaev model, quantum chaos, and gravity duals.  United States.  https://doi.org/10.1103/PhysRevD.103.106002

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                    García-García, Antonio M., Jia, Yiyang, Rosa, Dario, and Verbaarschot, Jacobus J. M. Mon .  
"Sparse Sachdev-Ye-Kitaev model, quantum chaos, and gravity duals".  United States.  https://doi.org/10.1103/PhysRevD.103.106002.

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@article{osti_1781178,

  title        = {Sparse Sachdev-Ye-Kitaev model, quantum chaos, and gravity duals},

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

  abstractNote = {We study a sparse Sachdev-Ye-Kitaev (SYK) model with N Majoranas where only ~ kN independent matrix elements are nonzero. We identify a minimum k ≳ 1 for quantum chaos to occur by a level statistics analysis. The spectral density in this region, and for a larger k, is still given by the Schwarzian prediction of the dense SYK model, though with renormalized parameters. Similar results are obtained for a beyond linear scaling with N of the number of nonzero matrix elements. This is a strong indication that this is the minimum connectivity for the sparse SYK model to still have a quantum gravity dual. We also find an intriguing exact relation between the leading correction to moments of the spectral density due to sparsity and the leading 1/d correction of Parisi’s U(1) lattice gauge theory in a d -dimensional hypercube. In the k → 1 limit, different disorder realizations of the sparse SYK model show emergent random matrix statistics that for fixed N can be in any universality class of the tenfold way. The agreement with random matrix statistics is restricted to short-range correlations, no more than a few level spacings, in particular in the tail of the spectrum. In addition, emergent discrete global symmetries in most of the disorder realizations for k slightly below one give rise to 2m-fold degenerate spectra, with m being a positive integer. For k = 3/4, we observe a large number of such emergent global symmetries with a maximum 28-fold degenerate spectra for N = 26.},

  doi          = {10.1103/PhysRevD.103.106002},

  journal      = {Physical Review D},

  number       = 10,

  volume       = 103,

  place        = {United States},

  year         = {Mon May 03 00:00:00 EDT 2021},

  month        = {Mon May 03 00:00:00 EDT 2021}

}

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Works referenced in this record:

Replica theory and large-D Josephson junction hypercubic models
journal, August 1995

Marinari, E.; Parisi, G.; Ritort, F.
Journal of Physics A: Mathematical and General, Vol. 28, Issue 16
DOI: 10.1088/0305-4470/28/16/008

The Distribution of Crossings of Chords Joining Pairs of 2n Points on a Circle
journal, January 1975

Riordan, John
Mathematics of Computation, Vol. 29, Issue 129
DOI: 10.2307/2005477

Spectral statistics of Erdős–Rényi graphs I: Local semicircle law
journal, May 2013

Erdős, László; Knowles, Antti; Yau, Horng-Tzer
The Annals of Probability, Vol. 41, Issue 3B
DOI: 10.1214/11-AOP734

Many-body localization in a finite-range Sachdev-Ye-Kitaev model and holography
journal, February 2019

García-García, Antonio M.; Tezuka, Masaki
Physical Review B, Vol. 99, Issue 5
DOI: 10.1103/PhysRevB.99.054202

NO2 jet cooled visible excitation spectrum: Vibronic chaos induced by the X̃ 2A1–Ã 2B2 interaction
journal, October 1991

Delon, A.; Jost, R.; Lombardi, M.
The Journal of Chemical Physics, Vol. 95, Issue 8
DOI: 10.1063/1.461620

Chaos on the hypercube
journal, November 2020

Jia, Yiyang; Verbaarschot, Jacobus J. M.
Journal of High Energy Physics, Vol. 2020, Issue 11
DOI: 10.1007/JHEP11(2020)154

Quantum Jackiw-Teitelboim gravity, Selberg trace formula, and random matrix theory
journal, December 2020

García-García, Antonio M.; Zacarías, Salomón
Physical Review Research, Vol. 2, Issue 4
DOI: 10.1103/PhysRevResearch.2.043310

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

Bertrand, Corentin L.; García-García, Antonio M.
Physical Review B, Vol. 94, Issue 14
DOI: 10.1103/PhysRevB.94.144201

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

Guhr, Thomas; Müller–Groeling, Axel; Weidenmüller, Hans A.
Physics Reports, Vol. 299, Issue 4-6
DOI: 10.1016/S0370-1573(97)00088-4

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

Altland, Alexander; Zirnbauer, Martin R.
Physical Review B, Vol. 55, Issue 2
DOI: 10.1103/PhysRevB.55.1142

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
DOI: 10.1007/JHEP06(2017)111

D-dimensional arrays of Josephson junctions, spin glasses and q-deformed harmonic oscillators
journal, December 1994

Parisi, G.
Journal of Physics A: Mathematical and General, Vol. 27, Issue 23
DOI: 10.1088/0305-4470/27/23/007

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

Luitz, David J.; Laflorencie, Nicolas; Alet, Fabien
Physical Review B, Vol. 91, Issue 8
DOI: 10.1103/PhysRevB.91.081103

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

Bohigas, O.; Flores, J.
Physics Letters B, Vol. 35, Issue 5
DOI: 10.1016/0370-2693(71)90399-6

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
DOI: 10.1103/PhysRevLett.70.3339

Nonuniversal Behavior of the $k$ -Body Embedded Gaussian Unitary Ensemble of Random Matrices
journal, June 2001

Benet, L.; Rupp, T.; Weidenmüller, H. A.
Physical Review Letters, Vol. 87, Issue 1
DOI: 10.1103/PhysRevLett.87.010601

Spectral density singularities, level statistics, and localization in a sparse random matrix ensemble
journal, January 1992

Evangelou, S. N.; Economou, E. N.
Physical Review Letters, Vol. 68, Issue 3
DOI: 10.1103/PhysRevLett.68.361

Replica variables, loop expansion, and spectral rigidity of random-matrix ensembles
journal, November 1984

Verbaarschot, J. J. M.; Zirnbauer, M. R.
Annals of Physics, Vol. 158, Issue 1
DOI: 10.1016/0003-4916(84)90240-9

Solving the frustrated spherical model with q -polynomials
journal, April 1998

Cappelli, Andrea; Colomo, Filippo
Journal of Physics A: Mathematical and General, Vol. 31, Issue 14
DOI: 10.1088/0305-4470/31/14/004

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
DOI: 10.1103/PhysRevB.63.134406

Spectral Statistics of Erdős-Rényi Graphs II: Eigenvalue Spacing and the Extreme Eigenvalues
journal, August 2012

Erdős, László; Knowles, Antti; Yau, Horng-Tzer
Communications in Mathematical Physics, Vol. 314, Issue 3
DOI: 10.1007/s00220-012-1527-7

Statistical properties of many-particle spectra
journal, November 1975

Mon, K. K.; French, J. B.
Annals of Physics, Vol. 95, Issue 1
DOI: 10.1016/0003-4916(75)90045-7

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

Density of states of a sparse random matrix
journal, March 1988

Rodgers, G. J.; Bray, A. J.
Physical Review B, Vol. 37, Issue 7
DOI: 10.1103/PhysRevB.37.3557

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

French, J. B.; Wong, S. S. M.
Physics Letters B, Vol. 33, Issue 7
DOI: 10.1016/0370-2693(70)90213-3

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

French, J. B.; Wong, S. S. M.
Physics Letters B, Vol. 35, Issue 1
DOI: 10.1016/0370-2693(71)90424-2

Localization and fluctuations of local spectral density on treelike structures with large connectivity: Application to the quasiparticle line shape in quantum dots
journal, November 1997

Mirlin, Alexander D.; Fyodorov, Yan V.
Physical Review B, Vol. 56, Issue 20
DOI: 10.1103/PhysRevB.56.13393

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

Alhassid, Y.; Levine, R. D.
Physical Review A, Vol. 46, Issue 8
DOI: 10.1103/PhysRevA.46.4650

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

Altshuler, Boris L.; Gefen, Yuval; Kamenev, Alex
Physical Review Letters, Vol. 78, Issue 14
DOI: 10.1103/PhysRevLett.78.2803

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

Atas, Y. Y.; Bogomolny, E.; Giraud, O.
Physical Review Letters, Vol. 110, Issue 8
DOI: 10.1103/PhysRevLett.110.084101

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

Bohigas, O.; Giannoni, M. J.; Schmit, C.
Physical Review Letters, Vol. 52, Issue 1
DOI: 10.1103/PhysRevLett.52.1

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

Localization in ensemble of sparse random matrices
journal, October 1991

Fyodorov, Yan; Mirlin, Alexander
Physical Review Letters, Vol. 67, Issue 15
DOI: 10.1103/PhysRevLett.67.2049

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

García-García, Antonio M.; Verbaarschot, Jacobus J. M.
Physical Review D, Vol. 96, Issue 6
DOI: 10.1103/PhysRevD.96.066012

Exact moments of the Sachdev-Ye-Kitaev model up to order 1/N2
journal, April 2018

García-García, Antonio M.; Jia, Yiyang; Verbaarschot, Jacobus J. M.
Journal of High Energy Physics, Vol. 2018, Issue 4
DOI: 10.1007/JHEP04(2018)146

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

Borgonovi, F.; Izrailev, F. M.; Santos, L. F.
Physics Reports, Vol. 626
DOI: 10.1016/j.physrep.2016.02.005

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

Torres-Herrera, E. J.; García-García, Antonio M.; Santos, Lea F.
Physical Review B, Vol. 97, Issue 6
DOI: 10.1103/PhysRevB.97.060303

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

Erdős, László; Schröder, Dominik
Mathematical Physics, Analysis and Geometry, Vol. 17, Issue 3-4
DOI: 10.1007/s11040-014-9164-3

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
DOI: 10.1016/j.nuclphysb.2017.06.012

A Graph-Theoretic Approach to a Communications Problem
journal, July 1966

Chartrand, Gary
SIAM Journal on Applied Mathematics, Vol. 14, Issue 4
DOI: 10.1137/0114065

Localization of interacting fermions at high temperature
journal, April 2007

Oganesyan, Vadim; Huse, David A.
Physical Review B, Vol. 75, Issue 15
DOI: 10.1103/PhysRevB.75.155111

Spectral asymmetry and Riemannian Geometry. I
journal, January 1975

Atiyah, M. F.; Patodi, V. K.; Singer, I. M.
Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 77, Issue 1
DOI: 10.1017/S0305004100049410

Lower dimensional gravity
journal, January 1985

Jackiw, Roman
Nuclear Physics B, Vol. 252
DOI: 10.1016/0550-3213(85)90448-1

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

Quantum chaos transition in a two-site Sachdev-Ye-Kitaev model dual to an eternal traversable wormhole
journal, July 2019

García-García, Antonio M.; Nosaka, Tomoki; Rosa, Dario
Physical Review D, Vol. 100, Issue 2
DOI: 10.1103/PhysRevD.100.026002

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
DOI: 10.1103/PhysRevD.94.126010

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
DOI: 10.1007/JHEP01(2017)138

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

Maldacena, Juan; Stanford, Douglas
Physical Review D, Vol. 94, Issue 10
DOI: 10.1103/PhysRevD.94.106002

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

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

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

Dyson, Freeman J.
Journal of Mathematical Physics, Vol. 3, Issue 6
DOI: 10.1063/1.1703862

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

Teitelboim, Claudio
Physics Letters B, Vol. 126, Issue 1-2
DOI: 10.1016/0370-2693(83)90012-6

Statistics of spectra of disordered systems near the metal-insulator transition
journal, May 1993

Shklovskii, B. I.; Shapiro, B.; Sears, B. R.
Physical Review B, Vol. 47, Issue 17
DOI: 10.1103/PhysRevB.47.11487

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

Ismail, Mourad E. H.; Stanton, Dennis; Viennot, Gérard
European Journal of Combinatorics, Vol. 8, Issue 4
DOI: 10.1016/S0195-6698(87)80046-X

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
DOI: 10.1103/PhysRevLett.120.241603

Random Graphs
journal, December 1959

Gilbert, E. N.
The Annals of Mathematical Statistics, Vol. 30, Issue 4
DOI: 10.1214/aoms/1177706098

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
DOI: 10.1103/PhysRevB.95.115150

Holographic Metals and the Fractionalized Fermi Liquid
journal, October 2010

Sachdev, Subir
Physical Review Letters, Vol. 105, Issue 15
DOI: 10.1103/PhysRevLett.105.151602

Quantum chaos, thermodynamics and black hole microstates in the mass deformed SYK model
journal, August 2020

Nosaka, Tomoki; Numasawa, Tokiro
Journal of High Energy Physics, Vol. 2020, Issue 8
DOI: 10.1007/JHEP08(2020)081

Spectral statistics of sparse Erdős–Rényi graph Laplacians
journal, February 2020

Huang, Jiaoyang; Landon, Benjamin
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 56, Issue 1
DOI: 10.1214/19-AIHP957

Periodic Table of the Ordinary and Supersymmetric Sachdev-Ye-Kitaev Models
journal, June 2020

Sun, Fadi; Ye, Jinwu
Physical Review Letters, Vol. 124, Issue 24
DOI: 10.1103/PhysRevLett.124.244101

Spectral fluctuations in the Sachdev-Ye-Kitaev model
journal, July 2020

Jia, Yiyang; Verbaarschot, Jacobus J. M.
Journal of High Energy Physics, Vol. 2020, Issue 7
DOI: 10.1007/JHEP07(2020)193

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
DOI: 10.1007/JHEP09(2018)041

Bulk eigenvalue statistics for random regular graphs
journal, November 2017

Bauerschmidt, Roland; Huang, Jiaoyang; Knowles, Antti
The Annals of Probability, Vol. 45, Issue 6A
DOI: 10.1214/16-AOP1145

Bulk universality of sparse random matrices
journal, December 2015

Huang, Jiaoyang; Landon, Benjamin; Yau, Horng-Tzer
Journal of Mathematical Physics, Vol. 56, Issue 12
DOI: 10.1063/1.4936139

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

Dyson, Freeman J.
Journal of Mathematical Physics, Vol. 3, Issue 1
DOI: 10.1063/1.1703773

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

Dyson, Freeman J.
Journal of Mathematical Physics, Vol. 3, Issue 1
DOI: 10.1063/1.1703774

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

Dyson, Freeman J.
Journal of Mathematical Physics, Vol. 3, Issue 1
DOI: 10.1063/1.1703775

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

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Title: Sparse Sachdev-Ye-Kitaev model, quantum chaos, and gravity duals

Abstract

Citation Formats

Replica theory and large-D Josephson junction hypercubic models journal, August 1995

The Distribution of Crossings of Chords Joining Pairs of 2n Points on a Circle journal, January 1975

Spectral statistics of Erdős–Rényi graphs I: Local semicircle law journal, May 2013

Many-body localization in a finite-range Sachdev-Ye-Kitaev model and holography journal, February 2019

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Quantum Jackiw-Teitelboim gravity, Selberg trace formula, and random matrix theory journal, December 2020

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

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

Supersymmetric SYK model and random matrix theory journal, June 2017

D-dimensional arrays of Josephson junctions, spin glasses and q-deformed harmonic oscillators journal, December 1994

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

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

Nonuniversal Behavior of the k -Body Embedded Gaussian Unitary Ensemble of Random Matrices journal, June 2001

Spectral density singularities, level statistics, and localization in a sparse random matrix ensemble journal, January 1992

Replica variables, loop expansion, and spectral rigidity of random-matrix ensembles journal, November 1984

Solving the frustrated spherical model with q -polynomials journal, April 1998

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

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Some random-matrix level and spacing distributions for fixed-particle-rank interactions
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Spectral autocorrelation function in the statistical theory of energy levels
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Quasiparticle Lifetime in a Finite System: A Nonperturbative Approach
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Distribution of the Ratio of Consecutive Level Spacings in Random Matrix Ensembles
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Conformal symmetry and its breaking in two-dimensional nearly anti-de Sitter space
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Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation Laws
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Black holes and random matrices
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Localization in ensemble of sparse random matrices
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Analytical spectral density of the Sachdev-Ye-Kitaev model at finite $N$
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Exact moments of the Sachdev-Ye-Kitaev model up to order 1/N2
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Quantum chaos and thermalization in isolated systems of interacting particles
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Generic dynamical features of quenched interacting quantum systems: Survival probability, density imbalance, and out-of-time-ordered correlator
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Phase Transition in the Density of States of Quantum Spin Glasses
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Lower dimensional gravity
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A bound on chaos
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Quantum chaos transition in a two-site Sachdev-Ye-Kitaev model dual to an eternal traversable wormhole
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Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
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Higher dimensional generalizations of the SYK model
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Gravitation and hamiltonian structure in two spacetime dimensions
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The Combinatorics of q-Hermite polynomials and the Askey—Wilson Integral
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Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model
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Random Graphs
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Quantum chaos, thermodynamics and black hole microstates in the mass deformed SYK model
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