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

Abstract

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 of $\sqrt{D}$ for $q>2$, with $D$ the total number of states.

arXiv comment47 pages, 19 figures. v2: minor corrections, version as published

References in corpus (55)

• A bound on chaos
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Black Holes and Random Matrices
• Holographic metals and the fractionalized Fermi liquid
• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• Semiclassical Foundation of Universality in Quantum Chaos
• Sachdev-Ye-Kitaev Model and Thermalization on the Boundary of Many-Body Localized Fermionic Symmetry Protected Topological States
• Semiclassical Theory of Chaotic Quantum Transport
• Almost-Hermitian Random Matrices: Crossover from Wigner-Dyson to Ginibre eigenvalue statistics
• Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos
• Analytical Spectral Density of the Sachdev-Ye-Kitaev Model at finite N
• Onset of Random Matrix Behavior in Scrambling Systems
• Random Matrices close to Hermitian or unitary: overview of methods and results
• Thouless and relaxation time scales in many-body quantum systems
• Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems
• Supersymmetric SYK model and random matrix theory
• Universality classes of non-Hermitian random matrices
• The spectral form factor is not self-averaging
• Anderson transition in three-dimensional systems with non-Hermitian disorder
• Non-Hermitian Random Matrix Theory and Lattice QCD with Chemical Potential
• Generic dynamical features of quenched interacting quantum systems: Survival probability, density imbalance and out-of-time-ordered correlator
• Phase Transition in the Density of States of Quantum Spin Glasses
• Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model
• Universality classes of the Anderson Transitions Driven by non-Hermitian Disorder
• Review of the k-Body Embedded Ensembles of Gaussian Random Matrices
• Complete random matrix classification of SYK models with $\mathcal{N}=0$, $1$ and $2$ supersymmetry
• Thermofield dynamics: Quantum Chaos versus Decoherence
• Euclidean wormhole in the SYK model
• Lindbladian dissipation of strongly-correlated quantum matter
• Random Lindblad Dynamics
• Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev Model
• Spectral Filtering Induced by Non-Hermitian Evolution with Balanced Gain and Loss: Enhancing Quantum Chaos
• Spectral Statistics of the Two-Body Random Ensemble Revisited
• Lindbladian dynamics of the Sachdev-Ye-Kitaev model
• Entanglement Entropy and Full Counting Statistics for $2d$-Rotating Trapped Fermions
• Emergent Replica Conformal Symmetry in Non-Hermitian SYK${}_2$ Chains
• Transfer matrix study of the Anderson transition in non-Hermitian systems
• Spectral Correlations from the Metal to the Mobility Edge
• Non-Universal Behavior of the k-Body Embedded Gaussian Unitary Ensemble of Random Matrices
• Integrable nonunitary open quantum circuits
• Periodic Table of SYK and supersymmetric SYK
• Spectral Properties of Disordered Interacting Non-Hermitian Systems
• Spectral rigidity of non-Hermitian symmetric random matrices near Anderson transition
• Spectral Fluctuations in the Sachdev-Ye-Kitaev Model
• Non-unitary dynamics of Sachdev-Ye-Kitaev chain
• From integrability to chaos in quantum Liouvillians
• Critical statistics for non-Hermitian matrices
• New universality classes of the non-Hermitian Dirac operator in QCD-like theories
• Large $N$ expansion of the moments and free energy of Sachdev-Ye-Kitaev model, and the enumeration of intersection graphs
• $Q$-Laguerre spectral density and quantum chaos in the Wishart-Sachdev-Ye-Kitaev model
• Multi-trace Correlators in the SYK Model and Non-geometric Wormholes
• Dissipative quantum dynamics, phase transitions and non-Hermitian random matrices
• Quantum Lyapunov exponents and complex spacing ratios: two measures of Dissipative Quantum Chaos

Cited by in corpus (16)

• Quantum Dynamics in Krylov Space: Methods and Applications
• Symmetry Classification of Many-Body Lindbladians: Tenfold Way and Beyond
• Non-Hermitian strongly interacting Dirac fermions: a quantum Monte-Carlo study
• Dynamical quantum phase transitions in SYK Lindbladians
• Non-Hermitian Hamiltonians Violate the Eigenstate Thermalization Hypothesis
• Robustness of quantum chaos and anomalous relaxation in open quantum circuits
• Entanglement Transition and Replica Wormhole in the Dissipative Sachdev-Ye-Kitaev Model
• Probing quantum chaos through singular-value correlations in sparse non-Hermitian SYK model
• Breakdown of the Quantum Distinction of Regular and Chaotic Classical Dynamics in Dissipative Systems
• Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes
• Two transitions in complex eigenvalue statistics: Hermiticity and integrability breaking
• Theory of Irreversibility in Quantum Many-Body Systems
• Universal hard-edge statistics of non-Hermitian random matrices
• Correspondence principle, dissipation, and Ginibre ensemble
• Error Threshold of SYK Codes from Strong-to-Weak Parity Symmetry Breaking
• Surmise for random matrices' level spacing distributions beyond nearest-neighbors