Light-cone spreading of perturbations and the butterfly effect in a classical spin chain

Abstract

We find that localised perturbations in a chaotic classical many-body system-- the classical Heisenberg We find that the effects of a localised perturbation in a chaotic classical many-body system--the classical Heisenberg chain at infinite temperature--spread ballistically with a finite speed even when the local spin dynamics is diffusive. We study two complementary aspects of this butterfly effect: the rapid growth of the perturbation, and its simultaneous ballistic (light-cone) spread, as characterised by the Lyapunov exponents and the butterfly speed respectively. We connect this to recent studies of the out-of-time-ordered commutators (OTOC), which have been proposed as an indicator of chaos in a quantum system. We provide a straightforward identification of the OTOC with a natural correlator in our system and demonstrate that many of its interesting qualitative features are present in the classical system. Finally, by analysing the scaling forms, we relate the growth, spread and propagation of the perturbation with the growth of one-dimensional interfaces described by the Kardar-Parisi-Zhang (KPZ) equation.

arXiv comment6 pages, 6 figures. Journal Ref. added: Physical Review Letters 121, 024101 (2018)

References in corpus (29)

• A bound on chaos
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Black holes and the butterfly effect
• Fast Scramblers
• Operator Spreading in Random Unitary Circuits
• Chaos in quantum channels
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Measuring the scrambling of quantum information
• Towards the fast scrambling conjecture
• Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
• Lieb-Robinson and the butterfly effect
• Slow scrambling in disordered quantum systems
• Scrambling and thermalization in a diffusive quantum many-body system
• Solvable model for a dynamical quantum phase transition from fast to slow scrambling
• Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
• Many-body chaos at weak coupling
• Weak Quantum Chaos
• Quantum chaos on a critical Fermi surface
• 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
• Energy diffusion and the butterfly effect in inhomogeneous Sachdev-Ye-Kitaev chains
• Largest Lyapunov exponents for lattices of interacting classical spins
• Spreading of Perturbations in Long-Range Interacting Classical Lattice Models
• The height distribution of the KPZ equation with sharp wedge initial condition: numerical evaluations
• Chronotopic Lyapunov Analysis: (I) a Comprehensive Characterization of 1D Systems
• Chronotopic Lyapunov Analysis: (II) towards a Unified Approach
• Driven Heisenberg Magnets: Nonequilibrium Criticality, Spatiotemporal Chaos and Control

Cited by in corpus (62)

• Velocity-dependent Lyapunov exponents in many-body quantum, semi-classical, and classical chaos
• Operator growth and eigenstate entanglement in an interacting integrable Floquet system
• Euclidean operator growth and quantum chaos
• Kardar-Parisi-Zhang universality from soft gauge modes
• Universality classes of spin transport in one-dimensional isotropic magnets: the onset of logarithmic anomalies
• Absence of fast scrambling in thermodynamically stable long-range interacting systems
• Temperature dependence of butterfly effect in a classical many-body system
• Hydrodynamics in lattice models with continuous non-Abelian symmetries
• Quantum Chaos and the Correspondence Principle
• A cavity-QED simulator of slow and fast scrambling
• Classical many-body chaos with and without quasiparticles
• Nonergodic Quantum Dynamics from Deformations of Classical Cellular Automata
• Regularization dependence of the OTOC. Which Lyapunov spectrum is the physical one?
• Quantum operator growth bounds for kicked tops and semiclassical spin chains
• Signature of Chaos and Delocalization in a Periodically Driven Many Body System : An Out-of-Time-Order Correlation Study
• Nonlinear Fluctuating Hydrodynamics for the Classical XXZ Spin Chain
• Intermittency, fluctuations and maximal chaos in an emergent universal state of active turbulence
• Many-body Chaos in Thermalised Fluids
• Quantum versus Classical Dynamics in Spin Models: Chains, Ladders, and Square Lattices
• Measurement-induced phase transition in a classical, chaotic many-body system
• Robustness of Kardar-Parisi-Zhang scaling in a classical integrable spin chain with broken integrability
• The tenfold way and many-body zero modes in the Sachdev-Ye-Kitaev model
• Spatio-temporal spread of perturbations in a driven dissipative Duffing chain: an OTOC approach
• Out of Time Ordered Quantum Dissipation
• Arresting classical many-body chaos by kinetic constraints
• Decay of spin-spin correlations in disordered quantum and classical spin chains
• Bridging the gap between classical and quantum many-body information dynamics
• Transport properties of the classical Toda chain: effect of a pinning potential
• Quantum Hydrodynamics in Spin Chains with Phase Space Methods
• Complexity of quantum motion and quantum-classical correspondence: A phase-space approach
• Butterfly Effect and Spatial Structure of Information Spreading in a Chaotic Cellular Automaton
• Many-body chaos near a thermal phase transition
• Fingerprint of chaos and quantum scars in kicked Dicke model: An out-of-time-order correlator study
• Transport, correlations, and chaos in a classical disordered anharmonic chain
• Dissipative Quantum Chaos unveiled by Stochastic Quantum Trajectories
• Spatio-temporal spread of perturbations in power-law models at low temperatures: Exact results for OTOC
• Dynamics and transport in the boundary-driven dissipative Klein-Gordon chain
• Characteristic, dynamic, and near saturation regions of Out-of-time-order correlation in Floquet Ising models
• Constrained Dynamics and Directed Percolation
• Quantum and Classical Dynamics with Random Permutation Circuits
• Self-trapping phenomenon, multistability and chaos in open anisotropic Dicke dimer
• Classical route to ergodicity and scarring in collective quantum systems
• Chaotic and quantum dynamics in driven-dissipative bosonic chains
• Prethermalization in aperiodically driven classical spin systems
• Semiclassical Limit of Measurement-Induced Transition in Many-Body Chaos in Integrable and Nonintegrable Oscillator Chains
• Emergence of a quasi-ergodic steady state in a dissipative Tavis-Cummings array
• Domain wall dynamics in classical spin chains: free propagation, subdiffusive spreading, and soliton emission
• Control of spatiotemporal chaos by stochastic resetting
• Out-of-time-ordered correlator in the one-dimensional Kuramoto-Sivashinsky and Kardar-Parisi-Zhang equations
• Spectral Form Factors of Topological Phases
• Manifestation of strange nonchaotic attractors in extended systems: A study through out-of-time-ordered correlators
• Dynamical regimes of finite temperature discrete nonlinear Schrödinger chain
• Kinetics of information scrambling in correlated electrons: disorder-driven transition from shock-wave to FKPP dynamics
• Many-body chaos and anomalous diffusion across thermal phase transitions in two dimensions
• Random Permutation Circuits Beyond Qubits are Quantum Chaotic
• Phase transition from localization to chaos in classical many-body system
• Lindblad quantum dynamics from correlation functions of classical spin chains
• Semiclassical analysis of spin dynamics in the non-Hermitian Hubbard model
• Localization of information driven by stochastic resetting
• Out-of-time-order correlators of nonlocal block-spin and random observables in integrable and nonintegrable spin chains
• Chaos and quantum regimes in $n$-photon driven, dissipative bosonic chains
• Uncertainty Growth in Stably Stratified Turbulence