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 ${\mathrm{AI}}^{†}$ and ${\mathrm{AII}}^{†}$, beyond the Ginibre ensembles. These results provide strong evidence of striking universal features in non-unitary many-body quantum chaos, which in all cases can be captured by nHSYK models with $q>2$.

38 pages, 14 figures, 8 tables. v2: references added, as published

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Cited by in corpus (63)

• Operator growth in open quantum systems: lessons from the dissipative SYK
• Quantum Dynamics in Krylov Space: Methods and Applications
• Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos
• Lindbladian dissipation of strongly-correlated quantum matter
• Non-Hermitian Topological Phases: Principles and Prospects
• Symmetry Classification of Many-Body Lindbladians: Tenfold Way and Beyond
• Lindbladian dynamics of the Sachdev-Ye-Kitaev model
• Non-Hermitian Floquet Topological Matter -- A Review
• Non-Hermitian Hamiltonian Deformations in Quantum Mechanics
• Non-Hermitian strongly interacting Dirac fermions: a quantum Monte-Carlo study
• Many-body quantum chaos and emergence of Ginibre ensemble
• Dynamical quantum phase transitions in SYK Lindbladians
• Spectral Properties of Disordered Interacting Non-Hermitian Systems
• Non-Hermitian Stark Many-Body Localization
• Keldysh Wormholes and Anomalous Relaxation in the Dissipative Sachdev-Ye-Kitaev Model
• Entanglement Entropy of Non-Hermitian Eigenstates and the Ginibre Ensemble
• Binary-coupling sparse SYK: an improved model of quantum chaos and holography
• Singular-Value Statistics of Non-Hermitian Random Matrices and Open Quantum Systems
• Level statistics of real eigenvalues in non-Hermitian systems
• Dynamical quantum ergodicity from energy level statistics
• Universality and its limits in non-Hermitian many-body quantum chaos using the Sachdev-Ye-Kitaev model
• Refined quantum Lyapunov exponents from replica out-of-time-order correlators
• Krylov space approach to Singular Value Decomposition in non-Hermitian systems
• Spacing distribution in the 2D Coulomb gas: Surmise and symmetry classes of non-Hermitian random matrices at non-integer $\beta$
• Field theory of non-Hermitian disordered systems
• $Q$-Laguerre spectral density and quantum chaos in the Wishart-Sachdev-Ye-Kitaev model
• From Ergodicity to Many-Body Localization in a One-Dimensional Interacting Non-Hermitian Stark System
• Quantum Chaos and Coherence: Random Parametric Quantum Channels
• Dissipative Quantum Chaos unveiled by Stochastic Quantum Trajectories
• Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes
• 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
• Stochastic Operator Variance: an observable to diagnose noise and scrambling
• Quantum jumps in driven-dissipative disordered many-body systems
• Multifractality of many-body non-Hermitian skin effect
• Eigenvector Correlations Across the Localisation Transition in non-Hermitian Power-Law Banded Random Matrices
• Singular Value Decomposition and Its Blind Spot for Quantum Chaos in Non-Hermitian Sachdev-Ye-Kitaev Models
• Classical route to ergodicity and scarring in collective quantum systems
• Replica Symmetry Breaking for the Integrable Two-Site Sachdev-Ye-Kitaev Model
• Diagnosing Quantum Many-body Chaos in Non-Hermitian Quantum Spin Chain via Krylov Complexity
• Electric conductivity in non-Hermitian holography
• Symmetry classes of dissipative topological insulators with edge dark state
• Unveiling Eigenstate Thermalization for Non-Hermitian systems
• Universal hard-edge statistics of non-Hermitian random matrices
• Higher-order gap ratios of singular values in open quantum systems
• Boundary-driven many-body phase transitions in a non-Hermitian disordered fermionic chain
• Transport and integrability-breaking in non-Hermitian many-body quantum systems
• Symmetry classes of classical stochastic processes
• Sixfold Way of Traversable Wormholes in the Sachdev-Ye-Kitaev Model
• Integrability versus chaos in the steady state of many-body open quantum systems
• Transient and steady-state chaos in dissipative quantum systems
• Time-dependent driving and topological protection in the fractional Josephson effect
• SYK model based $\beta$ regime dependent two-qubit dynamical wormhole-inspired teleportation protocol simulation
• Correspondence principle, dissipation, and Ginibre ensemble
• Non-Hermitian topological superconductivity with symmetry-enriched spectral and eigenstate features
• Symmetry classification correspondence between quadratic Lindbladians and their steady states
• Non-Hermitian gravitational effects on Bose-Einstein condensate
• PT -symmetry breaking and universal spectral statistics in quantum kicked rotors
• Spectral statistics and energy-gap scaling in $k-$local spin Hamiltonians
• Non-linear sigma models for non-Hermitian random matrices in symmetry classes AI${}^{†}$ and AII${}^{†}$
• Euclidean-to-Lorentzian wormhole transition and gravitational symmetry breaking in the Sachdev-Ye-Kitaev model
• Entanglement production in the Sachdev-Ye-Kitaev Model and its variants