Out-of-Time-Order correlators in driven conformal field theories

Abstract

We compute Out-of-Time-Order correlators (OTOCs) for conformal field theories (CFTs) subjected to either continuous or discrete periodic drive protocols. This is achieved by an appropriate analytic continuation of the stroboscopic time. After detailing the general structure, we perform explicit calculations in large-$c$ CFTs where we find that OTOCs display an exponential, an oscillatory and a power-law behaviour in the heating phase, the non-heating phase and on the phase boundary, respectively. In contrast to this, for the Ising CFT representing an integrable model, OTOCs never display such exponential growth. This observation hints towards how OTOCs can demarcate between integrable and chaotic CFT models subjected to a periodic drive. We further explore properties of the light-cone which is characterized by the corresponding butterfly velocity as well as the Lyapunov exponent. Interestingly, as a consequence of the spatial inhomogeneity introduced by the drive, the butterfly velocity, in these systems, has an explicit dependence on the initial location of the operators. We chart out the dependence of the Lyapunov exponent and the butterfly velocities on the frequency and amplitude of the drive for both protocols and discuss the fixed point structure which differentiates such driven CFTs from their un-driven counterparts.

arXiv comment34 pages, 6 figures, references added, minor corrections

References in corpus (93)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Nonequilibrium dynamics of closed interacting quantum systems
• Probing many-body dynamics on a 51-atom quantum simulator
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• A bound on chaos
• Floquet Topological Insulator in Semiconductor Quantum Wells
• A quantum gas microscope - detecting single atoms in a Hubbard regime optical lattice
• Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
• Topological characterization of periodically-driven quantum systems
• The Magnus expansion and some of its applications
• Observation of a Discrete Time Crystal
• Transport properties of non-equilibrium systems under the application of light: Photo-induced quantum Hall insulators without Landau levels
• Floquet Time Crystals
• Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate
• On the phase structure of driven quantum systems
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Probing the Superfluid to Mott Insulator Transition at the Single Atom Level
• Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
• Dynamical quantum phase transitions: a review
• Conformal Four Point Functions and the Operator Product Expansion
• Two-dimensional conformal field theory and the butterfly effect
• High-fidelity control and entanglement of Rydberg atom qubits
• Universality of Long-Distance AdS Physics from the CFT Bootstrap
• Topological singularities and the general classification of Floquet-Bloch systems
• Floquet generation of Majorana end modes and topological invariants
• Many-body energy localization transition in periodically driven systems
• Effective Theory of Floquet Topological Transitions
• Quantum phase transitions in transverse field spin models: from statistical physics to quantum information
• Vacuum States for AdS_2 Black Holes
• Exotic Freezing of Response in Quantum Many-Body System
• Collapse and revival of quantum many-body scars via Floquet engineering
• Scattering Theory for Floquet-Bloch States
• Locality, Quantum Fluctuations, and Scrambling
• Universal scaling in fast quantum quenches in conformal field theories
• Logarithmically Slow Relaxation in Quasi-Periodically Driven Random Spin Chains
• Dynamics of the vacuum state in a periodically driven Rydberg chain
• Dynamical localization in a chain of hard core bosons under a periodic driving
• Transverse Ising Chain under Periodic Instantaneous Quenches: Dynamical Many-Body Freezing and Emergence of Solitary Oscillation
• Entanglement generation in periodically driven integrable systems: dynamical phase transitions and steady state
• Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories: Part I
• Freezing a Quantum Magnet by Repeated Quantum Interference: An Experimental Realization
• A two-way approach to out-of-time-order correlators
• Random multipolar driving: tunably slow heating through spectral engineering
• Scrambling without chaos in RCFT
• Aperiodically driven integrable systems and their emergent steady states
• Emergent Black Hole Dynamics in Critical Floquet Systems
• Absence of dynamical localization in interacting driven systems
• Analytic approaches to periodically driven closed quantum systems: Methods and Applications
• Quasi-periodically driven quantum systems
• Geometric approach to inhomogeneous Floquet systems
• Effects of interactions on periodically driven dynamically localized systems
• Restoring coherence via aperiodic drives in a many-body quantum system
• Effects of periodic kicking on dispersion and wave packet dynamics in graphene
• Floquet conformal field theories with generally deformed Hamiltonians
• Dynamic freezing of strongly correlated ultracold bosons
• Extraction of conformal data in critical quantum spin chains using the Koo-Saleur formula
• Real Time Dynamics in Low Point Correlators in 2d BCFT
• Sine-square deformation and Mobius quantization of two-dimensional conformal field theory
• Fractional Statistics and the Butterfly Effect
• Quantum Lyapunov Spectrum
• The fine structure of heating in a quasiperiodically driven critical quantum system
• Non-equilibrium dynamics of quantum systems: order parameter evolution, defect generation, and qubit transfer
• Classification of $S{L}_2$ deformed Floquet Conformal Field Theories
• Maximum group velocity in a one-dimensional model with a sinusoidally varying staggered potential
• Low-frequency phase diagram of irradiated graphene and periodically driven spin-1/2 $XY$ chain
• Nonadiabatic charge pumping by oscillating potentials in one dimension: results for infinite system and finite ring
• Signature of Chaos and Delocalization in a Periodically Driven Many Body System : An Out-of-Time-Order Correlation Study
• Rigorous Bounds on the Heating Rate in Thue-Morse Quasiperiodically and Randomly Driven Quantum Many-Body Systems
• Periodically driven integrable systems with long-range pair potentials
• Adiabatic perturbation theory: from Landau-Zener problem to quenching through a quantum critical point
• Signatures and conditions for phase band crossings in periodically driven integrable systems
• Dynamics of quasiperiodically driven spin systems
• (Quasi)Periodic revivals in periodically driven interacting quantum systems
• A Floquet perturbation theory for periodically driven weakly-interacting fermions
• Floquet Scalar Dynamics in Global AdS
• Thermalization and chaos in QED${}_3$
• Dynamical relaxation of correlators in periodically driven integrable quantum systems
• Rotating Black Holes in AdS, Extremality and Chaos
• Dynamical crossover behavior in the relaxation of quenched quantum many-body systems
• Driven Holographic CFTs
• Conformal Floquet dynamics with a continuous drive protocol
• Slow scrambling in extremal BTZ and microstate geometries
• Dynamical Transition for a class of integrable models coupled to a bath
• The Real-Time Correlation Function of Floquet Conformal Fields
• Fast Scrambling due to Rotating Shockwaves in BTZ
• Localized states in global AdS
• Gravitational wave driving of a gapped holographic system
• Measuring out-of-time-ordered correlation functions with a single impurity qubit in a bosonic Josephson junction
• Out-of-Time-Order Correlation Functions for Unitary Minimal Models
• Oscillating Shells and Oscillating Balls in AdS
• Strings, Branes, Schwarzian Action and Maximal Chaos
• Critical Quenches, OTOCs and Early-Time Chaos

Cited by in corpus (11)

• State Dependence of Krylov Complexity in $2d$ CFTs
• Entanglement and geometry from subalgebras of the Virasoro algebra
• Scrambling and Recovery of Quantum Information in Inhomogeneous Quenches in Two-dimensional Conformal Field Theories
• Chaos and operator growth in 2d CFT
• Exactly solvable non-unitary time evolution in quantum critical systems I: Effect of complex spacetime metrics
• Entanglement wedge method, out-of-time-ordered correlators, and pole skipping
• Floquet engineered inhomogeneous quantum chaos in critical systems
• Phase Transitions in Quasi-Periodically Driven Quantum Critical Systems: Analytical Results
• 3D $\mathcal{N}=1$ supergravity from Virasoro TQFT: Gravitational partition function and Out-of-time-order correlator
• JT gravity and near-extremal thermodynamics for Kerr black holes in $Ad{S}_{4,5}$ for rotating perturbations
• Inhomogeneous Quantum Quenches of Conformal Field Theory with Boundaries