Quantum chaos in the Brownian SYK model with large finite $N$: OTOCs and tripartite information

Abstract

We consider the Brownian SYK model of $N$ interacting Majorana fermions, with random couplings that are taken to vary independently at each time. We study the out-of-time-ordered correlators (OTOCs) of arbitrary observables and the Rényi-$2$ tripartite information of the unitary evolution operator, which were proposed as diagnostic tools for quantum chaos and scrambling, respectively. We show that their averaged dynamics can be studied as a quench problem at imaginary times in a model of $N$ qudits, where the Hamiltonian displays site-permutational symmetry. By exploiting a description in terms of bosonic collective modes, we show that for the quantities of interest the dynamics takes place in a subspace of the effective Hilbert space whose dimension grows either linearly or quadratically with $N$, allowing us to perform numerically exact calculations up to $N=10^6$. We analyze in detail the interesting features of the OTOCs, including their dependence on the chosen observables, and of the tripartite information. We observe explicitly the emergence of a scrambling time $t^{\ast }\sim \ln N$ controlling the onset of both chaotic and scrambling behavior, after which we characterize the exponential decay of the quantities of interest to the corresponding Haar scrambled values.

arXiv comment25 pages, 13 figures

References in corpus (91)

• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• A bound on chaos
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• Black holes and the butterfly effect
• Black holes as mirrors: quantum information in random subsystems
• Fast Scramblers
• Time Evolution of Entanglement Entropy from Black Hole Interiors
• Operator Spreading in Random Unitary Circuits
• Chaos in quantum channels
• The Spectrum in the Sachdev-Ye-Kitaev Model
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Localized shocks
• Complexity, action, and black holes
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
• Multiple Shocks
• Thermoelectric transport in disordered metals without quasiparticles: the SYK models and holography
• Towards the fast scrambling conjecture
• Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
• Entanglement Tsunami: Universal Scaling in Holographic Thermalization
• Evenly distributed unitaries: on the structure of unitary designs
• Verified Quantum Information Scrambling
• Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• Random Quantum Circuits are Approximate 2-designs
• Lieb-Robinson and the butterfly effect
• Local random quantum circuits are approximate polynomial-designs
• Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation
• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
• Solution of a minimal model for many-body quantum chaos
• Emergent statistical mechanics of entanglement in random unitary circuits
• A strongly correlated metal built from Sachdev-Ye-Kitaev models
• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• Slow scrambling in disordered quantum systems
• Random Quantum Circuits and Pseudo-Random Operators: Theory and Applications
• Spectral statistics in spatially extended chaotic quantum many-body systems
• Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
• Operator space entanglement entropy in transverse Ising chain
• Numerical study of fermion and boson models with infinite-range random interactions
• Scrambling and entanglement spreading in long-range spin chains
• Power-law out of time order correlation functions in the SYK model
• Operator growth in the SYK model
• Out-of-time-ordered correlators in quantum Ising chain
• Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems
• Entanglement entropy of two disjoint blocks in XY chains
• Analytical Spectral Density of the Sachdev-Ye-Kitaev Model at finite N
• Many-body quantum chaos: Analytic connection to random matrix theory
• Onset of Random Matrix Behavior in Scrambling Systems
• Weak Quantum Chaos
• Quantum chaos on a critical Fermi surface
• Jarzynski-like equality for the out-of-time-ordered correlator
• Quantum Epidemiology: Operator Growth, Thermal Effects, and SYK
• Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1+1d
• Efficient Generation of Generic Entanglement
• Translationally invariant non-Fermi liquid metals with critical Fermi-surfaces: Solvable models
• Locality, Quantum Fluctuations, and Scrambling
• Out-of-Time-Ordered-Correlator Quasiprobabilities Robustly Witness Scrambling
• Spread of entanglement in a Sachdev-Ye-Kitaev chain
• Out-of-time-ordered density correlators in Luttinger liquids
• Scrambling of Quantum Information in Quantum Many-Body Systems
• Convergence Conditions for Random Quantum Circuits
• Convergence rates for arbitrary statistical moments of random quantum circuits
• On reduced density matrices for disjoint subsystems
• Efficient unitary designs with nearly time-independent Hamiltonian dynamics
• Exact convergence times for generation of random bipartite entanglement
• Emergence of typical entanglement in two-party random processes
• Operator Dynamics in Brownian Quantum Circuit
• Finite-size scaling of out-of-time-ordered correlators at late times
• Fast scrambling on sparse graphs
• Localization with random time-periodic quantum circuits
• Tripartite mutual information, entanglement, and scrambling in permutation symmetric systems with an application to quantum chaos
• Quantum chaos dynamics in long-range power law interaction systems
• Driven quantum dynamics: will it blend?
• Exact out-of-time-ordered correlation functions for an interacting lattice fermion model
• Does the SYK model have a spin glass phase?
• Mixing properties of stochastic quantum Hamiltonians
• Entanglement structure of current-driven diffusive fermion systems
• Exact moments of the Sachdev-Ye-Kitaev model up to order $1/N^2$
• Slow growth of out-of-time-order correlators and entanglement in integrable disordered systems
• Comment on the paper "Random Quantum Circuits are Approximate 2-designs"
• Optimal two-qubit gate for generation of random bipartite entanglement
• Efficiency of Producing Random Unitary Matrices with Quantum Circuits
• Out-of-time-ordered correlators in short-range and long-range hard-core boson models and in the Luttinger-liquid model
• Universal scrambling in gapless quantum spin chains
• Logarithmic spreading of out-of-time-ordered correlators without many-body localization
• Characterizing eigenstate thermalization via measures in the Fock space of operators
• Chaos and High Temperature Pure State Thermalization

Cited by in corpus (69)

• Exact dynamics in dual-unitary quantum circuits
• SYK meets non-Hermiticity II: measurement-induced phase transition
• Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits
• Scrambling in Random Unitary Circuits: Exact Results
• Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial
• Dynamical purification and the emergence of quantum state designs from the projected ensemble
• Nonlinear sigma models for monitored dynamics of free fermions
• A Random Unitary Circuit Model for Black Hole Evaporation
• A two-way approach to out-of-time-order correlators
• Scrambling is Necessary but Not Sufficient for Chaos
• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54
• Subleading Weingartens
• Emergent Replica Conformal Symmetry in Non-Hermitian SYK${}_2$ Chains
• Universal Entanglement Transitions of Free Fermions with Long-range Non-unitary Dynamics
• Entanglement distribution in the Quantum Symmetric Simple Exclusion Process
• Tripartite information, scrambling, and the role of Hilbert space partitioning in quantum lattice models
• Scrambling Ability of Quantum Neural Networks Architectures
• Non-unitary dynamics of Sachdev-Ye-Kitaev chain
• Many-body quantum dynamics slows down at low density
• Monitored fermions with conserved $\mathrm{U}(1)$ charge
• The Generalized OTOC from Supersymmetric Quantum Mechanics: Study of Random Fluctuations from Eigenstate Representation of Correlation Functions
• Dynamical Transition of Operator Size Growth in Quantum Systems Embedded in an Environment
• Note on entropy dynamics in the Brownian SYK model
• Resource theory of quantum uncomplexity
• Sachdev-Ye-Kitaev model on a noisy quantum computer
• Information Scrambling and Entanglement Dynamics of Complex Brownian Sachdev-Ye-Kitaev Models
• Hilbert space delocalization under random unitary circuits
• Information Scrambling with Conservation Laws
• The Timescales of Quantum Breaking
• Scrambling and Many-Body Localization in the XXZ-Chain
• An obstacle to sub-AdS holography for SYK-like models
• Designs via Free Probability
• Emergent Symmetry in Brownian SYK Models and Charge Dependent Scrambling
• Analytical results for the entanglement dynamics of disjoint blocks in the XY spin chain
• Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications
• Sachdev-Ye-Kitaev circuits for braiding and charging Majorana zero modes
• Signatures of quantum chaos in an out-of-time-order tensor
• Quantum information scrambling in the presence of weak and strong thermalization
• Multipartite information of free fermions on Hamming graphs
• Entanglement asymmetry dynamics in random quantum circuits
• Coarse-grained Entanglement and Operator Growth in Anomalous Dynamics
• Operator Size Distribution in Large $N$ Quantum Mechanics of Majorana Fermions
• Universality in the tripartite information after global quenches
• Charge transport, information scrambling and quantum operator-coherence in a many-body system with U(1) symmetry
• Entanglement dynamics of thermofield double states in integrable models
• Universality in the tripartite information after global quenches: (generalised) quantum XY models
• Excitation Transmission through a non-Hermitian traversable wormhole
• Onset of scrambling as a dynamical transition in tunable-range quantum circuits
• Dynamics of operator size distribution in q-local quantum Brownian SYK and spin models
• Approximate inverse measurement channel for shallow shadows
• Field theory for monitored Brownian SYK clusters
• Entanglement dynamics and Page curves in random permutation circuits
• Operator growth and black hole formation
• Noise Induced Universal Diffusive Transport in Fermionic Chains
• Universality in the tripartite information after global quenches: spin flip and semilocal charges
• Scrambling Transition in Free Fermion Systems Induced by a Single Impurity
• Efficient circular Dyson Brownian motion algorithm
• Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling
• Hierarchical analytical approach to universal spectral correlations in Brownian Quantum Chaos
• Entanglement dynamics from universal low-lying modes
• Non-Universality from Conserved Superoperators in Unitary Circuits
• Anatomy of information scrambling and decoherence in the integrable Sachdev-Ye-Kitaev model
• Chaos-protected locality
• Dynamics in the presence of local symmetry-breaking impurities
• Krylov complexity of many-body localization: Operator localization in Krylov basis
• Domain-wall melting in all-to-all QSSEP from random-matrix theory
• Diagnosing chaos with projected ensembles of process tensors
• Hybrid Brownian SYK-Hubbard Model: from Spectral Function to Quantum Chaos