Semiclassical echo dynamics in the Sachdev-Ye-Kitaev model

Abstract

The existence of a quantum butterfly effect in the form of exponential sensitivity to small perturbations has been under debate for a long time. Lately, this question gained increased interest due to the proposal to probe chaotic dynamics and scrambling using out-of-time-order correlators. In this work we study echo dynamics in the Sachdev-Ye-Kitaev model under effective time reversal in a semiclassical approach. We demonstrate that small imperfections introduced in the time-reversal procedure result in an exponential divergence from the perfect echo, which allows to identify a Lyapunov exponent ${\lambda }_L$. In particular, we find that ${\lambda }_L$ is twice the Lyapunov exponent of the semiclassical equations of motion. This behavior is attributed to the growth of an out-of-time-order double commutator that resembles an out-of-time-order correlator.

arXiv comment6+7 pages, 3+7 figures

References in corpus (38)

• 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 as mirrors: quantum information in random subsystems
• Fast Scramblers
• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Exploring the many-body localization transition in two dimensions
• Dynamics of Loschmidt echoes and fidelity decay
• Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
• Phase space representation of quantum dynamics
• Multiple Shocks
• Fermionic transport in a homogeneous Hubbard model: Out-of-equilibrium dynamics with ultracold atoms
• Holographic metals and the fractionalized Fermi liquid
• Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
• Out-of-Time-Order Correlation for Many-Body Localization
• Probing Slow Relaxation and Many-Body Localization in Two-Dimensional Quasi-Periodic Systems
• Slow scrambling in disordered quantum systems
• Out-of-time-ordered correlators in many-body localized systems
• Scrambling and thermalization in a diffusive quantum many-body system
• Operator growth in the SYK model
• Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom
• Out-of-time-order correlations in many-body localized and thermal phases
• Velocity-dependent Lyapunov exponents in many-body quantum, semi-classical, and classical chaos
• Quantum quench of the Sachdev-Ye-Kitaev Model
• Out-of-Time-Order Correlation at a Quantum Phase Transition
• Quantum butterfly effect in weakly interacting diffusive metals
• Scrambling of Quantum Information in Quantum Many-Body Systems
• Phase ordering kinetics of the Bose gas
• Non-adiabacity and large flucutations in a many particle Landau Zener problem
• Absence of exponential sensitivity to small perturbations in nonintegrable systems of spins 1/2
• Nonequilibrium dynamics of spin-boson models from phase space methods
• Semiclassical approach to Dynamics of Interacting Fermions
• Sensitivity to small perturbations in systems of large quantum spins
• Irreversible dynamics in quantum many-body systems
• Extracting Lyapunov exponents from the echo dynamics of Bose-Einstein condensates on a lattice
• Proliferation of effective interactions: decoherence-induced equilibration in a closed many-body system
• Effective time reversal and echo dynamics in the transverse field Ising model

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• Positive quantum Lyapunov exponents in experimental systems with a regular classical limit
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• Minimal Model for Fast Scrambling
• A generalized phase space approach for solving quantum spin dynamics
• A cavity-QED simulator of slow and fast scrambling
• Scrambling in strongly chaotic weakly coupled bipartite systems: Universality beyond the Ehrenfest time-scale
• Coherence requirements for quantum communication from hybrid circuit dynamics
• Saddle-point scrambling without thermalisation
• Semiclassical roots of universality in many-body quantum chaos
• Tripartite information, scrambling, and the role of Hilbert space partitioning in quantum lattice models
• Chaos in a classical limit of the Sachdev-Ye-Kitaev model
• Classical and quantum chaos in a three-mode bosonic system
• Universal Dynamics of Stochastically Driven Quantum Impurities
• Quantum echo dynamics in the Sherrington-Kirkpatrick model
• Out-of-time-order correlator in the quantum Rabi model
• Variational quantum dynamics of two-dimensional rotor models
• Quantum Hydrodynamics in Spin Chains with Phase Space Methods
• Thermalisation in a Bose-Hubbard dimer with modulated tunneling
• Semiclassical dynamics of a disordered two-dimensional Hubbard model with long-range interactions
• Performance evaluation of the discrete truncated Wigner approximation for quench dynamics of quantum spin systems with long-range interactions
• Quantum chaos and thermalization in the two-mode Dicke model
• Semiclassical bounds on dynamics of two-dimensional interacting disordered fermions
• Nonequilibrium many-body quantum dynamics: from full random matrices to real systems
• Systematic large flavor fTWA approach to interaction quenches in the Hubbard model
• Directional scrambling of quantum information in helical multiferroics
• Persistent many-body quantum echoes
• Universality in Non-Equilibrium Quantum Systems
• Classical periodic trajectories and quantum scars in many-spin systems
• Dynamical Quantum Phase Transitions and Many-Body Backflow in Open Quantum Systems