Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model

García-García, Antonio M.; Sá, Lucas; Verbaarschot, Jacobus J. M.

doi:10.1103/PhysRevX.12.021040

Title: Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model

Abstract

Spectral correlations are a powerful tool to study the dynamics of quantum many-body systems. For Hermitian Hamiltonians, quantum chaotic motion is related to random matrix theory spectral correlations. Based on recent progress in the application of spectral analysis to non-Hermitian quantum systems, we show that local level statistics, which probe the dynamics around the Heisenberg time, of a non-Hermitian q -body Sachdev-Ye-Kitev (nHSYK) model with N Majorana fermions, and its chiral and complex-fermion extensions, are also well described by random matrix theory for q > 2, while for q = 2, they are given by the equivalent of Poisson statistics. For that comparison, we combine exact diagonalization numerical techniques with analytical results obtained for some of the random matrix spectral observables. Moreover, depending on q and N, we identify 19 out of the 38 non-Hermitian universality classes in the nHSYK model, including those corresponding to the tenfold way. In particular, we realize explicitly 14 out of the 15 universality classes corresponding to non-pseudo-Hermitian Hamiltonians that involve universal bulk correlations of classes AI^† and AII^†, beyond the Ginibre ensembles. These results provide strong evidence of striking universal features in nonunitary many-body quantum chaos, which in all cases can be captured bymore » nHSYK models with q > 2.« less

Authors:

García-García, Antonio M.;

; Verbaarschot, Jacobus J. M.

Publication Date:: Wed May 18 00:00:00 EDT 2022

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

Sponsoring Org.:: USDOE Office of Science (SC); National Natural Science Foundation of China (NSFC); National Key Research and Development Program of China; Fundação Para A Ciência e Tecnologia (FCT)

OSTI Identifier:: 1868389

Alternate Identifier(s):: OSTI ID: 1980365; OSTI ID: 2280815

Grant/Contract Number:: FAG-88FR40388; FG02-88ER40388; 11874259; SFRH/BD/147477/2019

Resource Type:: Published Article

Journal Name:: Physical Review. X

Additional Journal Information:: Journal Name: Physical Review. X Journal Volume: 12 Journal Issue: 2; Journal ID: ISSN 2160-3308

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; dissipative dynamics; open quantum systems; quantum chaos; quantum gravity; quantum statistical mechanics; strongly correlated systems; random matrix theory; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats


                    García-García, Antonio M., Sá, Lucas, and Verbaarschot, Jacobus J. M. Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model.  United States: N. p., 2022. 
Web.  doi:10.1103/PhysRevX.12.021040.

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                    García-García, Antonio M., Sá, Lucas, & Verbaarschot, Jacobus J. M. Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model.  United States.  https://doi.org/10.1103/PhysRevX.12.021040

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                    García-García, Antonio M., Sá, Lucas, and Verbaarschot, Jacobus J. M. Wed .  
"Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model".  United States.  https://doi.org/10.1103/PhysRevX.12.021040.

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@article{osti_1868389,

  title        = {Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model},

  author       = {García-García, Antonio M. and Sá, Lucas and Verbaarschot, Jacobus J. M.},

  abstractNote = {Spectral correlations are a powerful tool to study the dynamics of quantum many-body systems. For Hermitian Hamiltonians, quantum chaotic motion is related to random matrix theory spectral correlations. Based on recent progress in the application of spectral analysis to non-Hermitian quantum systems, we show that local level statistics, which probe the dynamics around the Heisenberg time, of a non-Hermitian q -body Sachdev-Ye-Kitev (nHSYK) model with N Majorana fermions, and its chiral and complex-fermion extensions, are also well described by random matrix theory for q > 2, while for q = 2, they are given by the equivalent of Poisson statistics. For that comparison, we combine exact diagonalization numerical techniques with analytical results obtained for some of the random matrix spectral observables. Moreover, depending on q and N, we identify 19 out of the 38 non-Hermitian universality classes in the nHSYK model, including those corresponding to the tenfold way. In particular, we realize explicitly 14 out of the 15 universality classes corresponding to non-pseudo-Hermitian Hamiltonians that involve universal bulk correlations of classes AI† and AII†, beyond the Ginibre ensembles. These results provide strong evidence of striking universal features in nonunitary many-body quantum chaos, which in all cases can be captured by nHSYK models with q > 2.},

  doi          = {10.1103/PhysRevX.12.021040},

  journal      = {Physical Review. X},

  number       = 2,

  volume       = 12,

  place        = {United States},

  year         = {Wed May 18 00:00:00 EDT 2022},

  month        = {Wed May 18 00:00:00 EDT 2022}

}

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Universality and its limits in non-Hermitian many-body quantum chaos using the Sachdev-Ye-Kitaev model

Journal Article García-García, Antonio M. ; Sá, Lucas ; Verbaarschot, Jacobus J. M. - Physical Review. D.

Spectral rigidity in Hermitian quantum chaotic systems signals the presence of dynamical universal features at timescales that can be much shorter than the Heisenberg time. We study the analog of this timescale in many-body non-Hermitian quantum chaos by a detailed analysis of long-range spectral correlators. For that purpose, we investigate the number variance and the spectral form factor of a non-Hermitian q-body Sachdev-Ye-Kitaev (nHSYK) model, which describes N fermions in zero spatial dimensions. After an analytical and numerical analysis of these spectral observables for non-Hermitian random matrices, and a careful unfolding, we find good agreement with the nHSYK model for q > 2 starting at a timescale that decreases sharply with q. The source of deviation from universality, identified analytically, is ensemble fluctuations not related to the quantum dynamics. For fixed q and large enough N, these fluctuations become dominant up until after the Heisenberg time, so that the spectral form factor is no longer useful for the study of quantum chaos. In all cases, our results point to a weakened or vanishing spectral rigidity that effectively delays the observation of full quantum ergodicity. We also show that the number variance displays nonstationary spectral correlations for both the nHSYK model and random matrices. This nonstationarity, also not related to the quantum dynamics, points to intrinsic limitations of these observables to describe the quantum chaotic motion. On the other hand, we introduce the local spectral form factor, which is shown to be stationary and not affected by collective fluctuations, and propose it as an effective diagnostic of non-Hermitian quantum chaos. For q = 2, we find saturation to Poisson statistics at a timescale of log D, compared to a scale ofmore »« less
https://doi.org/10.1103/PhysRevD.107.066007
Sparse Sachdev-Ye-Kitaev model, quantum chaos, and gravity duals

Journal Article García-García, Antonio M. ; Jia, Yiyang ; Rosa, Dario ; ... - Physical Review D

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 havemore »« less
https://doi.org/10.1103/PhysRevD.103.106002
Dominance of Replica Off-Diagonal Configurations and Phase Transitions in a $P T$ Symmetric Sachdev-Ye-Kitaev Model

Journal Article García-García, Antonio M. ; Jia, Yiyang ; Rosa, Dario ; ... - Physical Review Letters

We show that, after ensemble averaging, the low temperature phase of a conjugate pair of uncoupled, quantum chaotic, non-Hermitian systems such as the Sachdev-Ye-Kitaev (SYK) model or the Ginibre ensemble of random matrices is dominated by saddle points that couple replicas and conjugate replicas. This results in a nearly flat free energy that terminates in a first-order phase transition. In the case of the SYK model, we show explicitly that the spectrum of the effective replica theory has a gap. These features are strikingly similar to those induced by wormholes in the gravity path integral which suggests a close relationmore »« less
https://doi.org/10.1103/PhysRevLett.128.081601
Replica symmetry breaking for the integrable two-site Sachdev–Ye–Kitaev model

Journal Article Jia, Yiyang ; Rosa, Dario ; Verbaarschot, Jacobus M. - Journal of Mathematical Physics

We analyze a two-body non-Hermitian two-site Sachdev–Ye–Kitaev (SYK) model with the couplings of one site complex conjugated to the other site. This model, with no explicit coupling between the sites, shows an infinite number of second-order phase transitions, which is a consequence of the factorization of the partition function into a product over Matsubara frequencies. We calculate the quenched free energy in two different ways: first in terms of the single-particle energies and second by solving the Schwinger–Dyson equations of the two-site model. The first calculation can be done entirely in terms of a one-site model. The conjugate replica entersmore »« less
https://doi.org/10.1063/5.0086748

Full Text Available
Replica symmetry breaking in random non-Hermitian systems

Journal Article García-García, Antonio M. ; Jia, Yiyang ; Rosa, Dario ; ... - Physical Review D

Recent studies have revealed intriguing similarities between the contribution of wormholes to the gravitational path integral and the phenomenon of replica symmetry breaking observed in spin glasses and other disordered systems. Interestingly, these configurations may also be important for the explanation of the information paradox of quantum black holes. Motivated by these developments, we investigate the thermodynamic properties of a PT-symmetric system composed of two random non-Hermitian Hamiltonians with no explicit coupling between them. After performing ensemble averaging, we identify numerically and analytically a robust first-order phase transition in the free energy of two models with quantum chaotic dynamics: themore »« less
https://doi.org/10.1103/PhysRevD.105.126027

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Title: Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model

Abstract

Citation Formats

Information in black hole radiation journal, December 1993

Many-body hierarchy of dissipative timescales in a quantum computer journal, June 2021

Condition of stochasticity in quantum nonlinear systems journal, May 1978

Level Clustering in the Regular Spectrum journal, September 1977

Symmetry Classes of Open Fermionic Quantum Matter journal, May 2021

Eigenvalue Density of the Non-Hermitian Wilson Dirac Operator journal, January 2012

Universal Spectra of Random Lindblad Operators journal, October 2019

Random matrix triality at nonzero chemical potential journal, December 1997

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

Random generators of Markovian evolution: A quantum-classical transition by superdecoherence journal, September 2021

Supersymmetric SYK model and random matrix theory journal, June 2017

The statistical theory of quantum dots journal, October 2000

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

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

Exact Results for the Two-Dimensional One-Component Plasma journal, February 1981

Statistical Ensembles of Complex, Quaternion, and Real Matrices journal, March 1965

Spacing ratio characterization of the spectra of directed random networks journal, December 2020

Extreme Decoherence and Quantum Chaos journal, January 2019

Factorization of correlation functions and the replica limit of the Toda lattice equation journal, April 2004

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

Real Spectra in Non-Hermitian Hamiltonians Having P T Symmetry journal, June 1998

The complex Laguerre symplectic ensemble of non-Hermitian matrices journal, December 2005

Integrable nonunitary open quantum circuits journal, March 2021

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

Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems journal, December 2019

Grassmann integration in stochastic quantum physics: The case of compound-nucleus scattering journal, December 1985

Localization Transitions in Non-Hermitian Quantum Mechanics journal, July 1996

Random-matrix theory for the Lindblad master equation journal, February 2021

Universality of spectra for interacting quantum chaotic systems journal, June 2010

Non-Hermitian physics journal, July 2020

Statistical properties of many-particle spectra journal, November 1975

Spectral Statistics of Non-Hermitian Matrices and Dissipative Quantum Chaos journal, October 2021

Problems with finite density simulations of lattice QCD journal, October 1986

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

Universality classes of non-Hermitian random matrices journal, June 2020

Non-unitary dynamics of Sachdev-Ye-Kitaev chain journal, January 2021

Gap probabilities in non-Hermitian random matrix theory journal, June 2009

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

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

Tenfold way and many-body zero modes in the Sachdev-Ye-Kitaev model journal, May 2019

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

Black holes and random matrices journal, May 2017

Quantum trajectories and open many-body quantum systems journal, March 2014

Universality classes of quantum chaotic dissipative systems journal, August 2019

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

Wigner surmise for Hermitian and non-Hermitian chiral random matrices journal, December 2009

Anderson transition in three-dimensional systems with non-Hermitian disorder journal, January 2020

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

Random quantum operations journal, January 2009

Spectral Gaps and Midgap States in Random Quantum Master Equations journal, December 2019

Localization of interacting fermions at high temperature journal, April 2007

Lower dimensional gravity journal, January 1985

Symmetry and Topology in Non-Hermitian Physics journal, October 2019

Random matrices beyond the Cartan classification journal, January 2008

Universal Results from an Alternate Random-Matrix Model for QCD with a Baryon Chemical Potential journal, November 2004

A bound on chaos journal, August 2016

Euclidean wormhole in the Sachdev-Ye-Kitaev model journal, February 2021

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

Q -Laguerre spectral density and quantum chaos in the Wishart-Sachdev-Ye-Kitaev model journal, January 2022

Hierarchy of Relaxation Timescales in Local Random Liouvillians journal, March 2020

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

Page curve from non-Markovianity journal, June 2021

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

Almost Hermitian Random Matrices: Crossover from Wigner-Dyson to Ginibre Eigenvalue Statistics journal, July 1997

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

Random-matrix physics: spectrum and strength fluctuations journal, July 1981

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

Keldysh field theory for driven open quantum systems journal, August 2016

Transfer matrix study of the Anderson transition in non-Hermitian systems journal, September 2021

Rotating trapped fermions in two dimensions and the complex Ginibre ensemble: Exact results for the entanglement entropy and number variance journal, February 2019

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

Random transition-rate matrices for the master equation journal, August 2009

Universality Classes of the Anderson Transitions Driven by Non-Hermitian Disorder journal, March 2021

Topological symmetry classes for non-Hermitian models and connections to the bosonic Bogoliubov–de Gennes equation journal, September 2018

Sachdev-Ye-Kitaev model and thermalization on the boundary of many-body localized fermionic symmetry-protected topological states journal, March 2017

Generating random quantum channels journal, June 2021

Information in black hole radiation
journal, December 1993

Many-body hierarchy of dissipative timescales in a quantum computer
journal, June 2021

Condition of stochasticity in quantum nonlinear systems
journal, May 1978

Level Clustering in the Regular Spectrum
journal, September 1977

Symmetry Classes of Open Fermionic Quantum Matter
journal, May 2021

Eigenvalue Density of the Non-Hermitian Wilson Dirac Operator
journal, January 2012

Universal Spectra of Random Lindblad Operators
journal, October 2019

Random matrix triality at nonzero chemical potential
journal, December 1997

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

Random generators of Markovian evolution: A quantum-classical transition by superdecoherence
journal, September 2021

Supersymmetric SYK model and random matrix theory
journal, June 2017

The statistical theory of quantum dots
journal, October 2000

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

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

Exact Results for the Two-Dimensional One-Component Plasma
journal, February 1981

Statistical Ensembles of Complex, Quaternion, and Real Matrices
journal, March 1965

Spacing ratio characterization of the spectra of directed random networks
journal, December 2020

Extreme Decoherence and Quantum Chaos
journal, January 2019

Factorization of correlation functions and the replica limit of the Toda lattice equation
journal, April 2004

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

Real Spectra in Non-Hermitian Hamiltonians Having $P T$ Symmetry
journal, June 1998

The complex Laguerre symplectic ensemble of non-Hermitian matrices
journal, December 2005

Integrable nonunitary open quantum circuits
journal, March 2021

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

Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems
journal, December 2019

Grassmann integration in stochastic quantum physics: The case of compound-nucleus scattering
journal, December 1985

Localization Transitions in Non-Hermitian Quantum Mechanics
journal, July 1996

Random-matrix theory for the Lindblad master equation
journal, February 2021

Universality of spectra for interacting quantum chaotic systems
journal, June 2010

Non-Hermitian physics
journal, July 2020

Statistical properties of many-particle spectra
journal, November 1975

Spectral Statistics of Non-Hermitian Matrices and Dissipative Quantum Chaos
journal, October 2021

Problems with finite density simulations of lattice QCD
journal, October 1986

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

Universality classes of non-Hermitian random matrices
journal, June 2020

Non-unitary dynamics of Sachdev-Ye-Kitaev chain
journal, January 2021

Gap probabilities in non-Hermitian random matrix theory
journal, June 2009

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

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

Tenfold way and many-body zero modes in the Sachdev-Ye-Kitaev model
journal, May 2019

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

Black holes and random matrices
journal, May 2017

Quantum trajectories and open many-body quantum systems
journal, March 2014

Universality classes of quantum chaotic dissipative systems
journal, August 2019

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

Wigner surmise for Hermitian and non-Hermitian chiral random matrices
journal, December 2009

Anderson transition in three-dimensional systems with non-Hermitian disorder
journal, January 2020

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

Random quantum operations
journal, January 2009

Spectral Gaps and Midgap States in Random Quantum Master Equations
journal, December 2019

Localization of interacting fermions at high temperature
journal, April 2007

Lower dimensional gravity
journal, January 1985

Symmetry and Topology in Non-Hermitian Physics
journal, October 2019

Random matrices beyond the Cartan classification
journal, January 2008

Universal Results from an Alternate Random-Matrix Model for QCD with a Baryon Chemical Potential
journal, November 2004

A bound on chaos
journal, August 2016

Euclidean wormhole in the Sachdev-Ye-Kitaev model
journal, February 2021

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

$Q$ -Laguerre spectral density and quantum chaos in the Wishart-Sachdev-Ye-Kitaev model
journal, January 2022

Hierarchy of Relaxation Timescales in Local Random Liouvillians
journal, March 2020

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

Page curve from non-Markovianity
journal, June 2021

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

Almost Hermitian Random Matrices: Crossover from Wigner-Dyson to Ginibre Eigenvalue Statistics
journal, July 1997

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

Random-matrix physics: spectrum and strength fluctuations
journal, July 1981

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

Keldysh field theory for driven open quantum systems
journal, August 2016

Transfer matrix study of the Anderson transition in non-Hermitian systems
journal, September 2021

Rotating trapped fermions in two dimensions and the complex Ginibre ensemble: Exact results for the entanglement entropy and number variance
journal, February 2019

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

Random transition-rate matrices for the master equation
journal, August 2009

Universality Classes of the Anderson Transitions Driven by Non-Hermitian Disorder
journal, March 2021

Topological symmetry classes for non-Hermitian models and connections to the bosonic Bogoliubov–de Gennes equation
journal, September 2018

Sachdev-Ye-Kitaev model and thermalization on the boundary of many-body localized fermionic symmetry-protected topological states
journal, March 2017

Generating random quantum channels
journal, June 2021

Emergent Replica Conformal Symmetry in Non-Hermitian SYK $_{2}$ Chains
journal, November 2021

New universality classes of the non-Hermitian Dirac operator in QCD-like theories
journal, July 2021

Tenfold Way for Quadratic Lindbladians
journal, January 2020