Dynamical Scaling Laws of Out-of-Time-Ordered Correlators
arXiv:1906.00533 · doi:10.1103/PhysRevB.100.195107
Abstract
The out-of-time-ordered correlator (OTOC) is central to the understanding of information scrambling in quantum many-body systems. In this work, we show that the OTOC in a quantum many-body system close to its critical point obeys dynamical scaling laws which are specified by a few universal critical exponents of the quantum critical point. Such scaling laws of the OTOC imply a universal form for the butterfly velocity of a chaotic system in the quantum critical region and allow one to locate the quantum critical point and extract all universal critical exponents of the quantum phase transitions. We numerically confirm the universality of the butterfly velocity in a chaotic model, namely the transverse axial next-nearest-neighbor Ising model, and show the feasibility of extracting the critical properties of quantum phase transitions from OTOC using the Lipkin-Meshkov-Glick (LMG) model.
arXiv comment6 pages, 2 figures
References in corpus (58)
- The density-matrix renormalization group in the age of matrix product states
- A bound on chaos
- Black holes and the butterfly effect
- Fast Scramblers
- Observation of entanglement propagation in a quantum many-body system
- Non-local propagation of correlations in long-range interacting quantum systems
- Chaos in quantum channels
- Localized shocks
- Universal digital quantum simulation with trapped ions
- Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
- Measuring the scrambling of quantum information
- Multiple Shocks
- Two-dimensional conformal field theory and the butterfly effect
- Theory of universal incoherent metallic transport
- Chaos and complexity by design
- Towards the fast scrambling conjecture
- Measuring out-of-time-order correlators on a nuclear magnetic resonance quantum simulator
- Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
- Verified Quantum Information Scrambling
- Lieb-Robinson and the butterfly effect
- Out-of-Time-Order Correlation for Many-Body Localization
- Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
- Dynamical phase transitions after quenches in non-integrable models
- Universal Charge Diffusion and the Butterfly Effect
- Out-of-time-ordered correlators in many-body localized systems
- 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
- Scrambling and entanglement spreading in long-range spin chains
- Out-of-time-ordered correlators in quantum Ising chain
- Detecting equilibrium and dynamical quantum phase transitions in Ising chains via out-of-time-ordered correlators
- Measurement of many-body chaos using a quantum clock
- Jarzynski-like equality for the out-of-time-ordered correlator
- The quasiprobability behind the out-of-time-ordered correlator
- Universal Diffusion in Incoherent Black Holes
- Quantum butterfly effect in weakly interacting diffusive metals
- Out-of-Time-Order Correlation at a Quantum Phase Transition
- Characterizing Many-Body Localization by Out-of-Time-Ordered Correlation
- Thermodynamics of quantum information scrambling
- Out-of-Time-Ordered-Correlator Quasiprobabilities Robustly Witness Scrambling
- Scrambling of Quantum Information in Quantum Many-Body Systems
- Charge diffusion and the butterfly effect in striped holographic matter
- Efficient decoding for the Hayden-Preskill protocol
- Universal Logarithmic Scrambling in Many Body Localization
- Information scrambling in chaotic systems with dissipation
- Resilience of scrambling measurements
- Detection of quantum phases via out-of-time-order correlators
- Exploring quantum signatures of chaos on a Floquet synthetic lattice
- Out-of-Time-Order Correlation in Marginal Many-Body Localized Systems
- Exact out-of-time-ordered correlation functions for an interacting lattice fermion model
- Out-of-time-order correlators in finite open systems
- Slow growth of out-of-time-order correlators and entanglement in integrable disordered systems
- Entropic uncertainty relations for quantum information scrambling
- Note on the butterfly effect in holographic superconductor models
- Conjecture on the Butterfly Velocity across a Quantum Phase Transition
- Operator scrambling and quantum chaos
- Prethermalization at Low Temperature: the Scent of Long-Range Order
- Holographic Butterfly Effect and Diffusion in Quantum Critical Region
- Universality in the Decay and Revival of Loschmidt Echoes
Cited by in corpus (18)
- Experimental Observation of Equilibrium and Dynamical Quantum Phase Transitions via Out-of-Time-Ordered Correlators
- Absence of fast scrambling in thermodynamically stable long-range interacting systems
- Out-of-time-order correlations and Floquet dynamical quantum phase transition
- The Generalized OTOC from Supersymmetric Quantum Mechanics: Study of Random Fluctuations from Eigenstate Representation of Correlation Functions
- Out-of-time-order correlators and quantum phase transitions in the Rabi and Dicke model
- Out-of-time-ordered correlator in non-Hermitian quantum systems
- Proposal for measuring out-of-time-ordered correlators at finite temperature with coupled spin chains
- The effect of chaos on the simulation of quantum critical phenomena in analog quantum simulators
- Dynamical crossover in the transient quench dynamics of short-range transverse field Ising models
- Quantum information scrambling in the presence of weak and strong thermalization
- Out of Time Order Correlations in the Quasi-Periodic Aubry-André model
- Quantum reservoir probing of quantum phase transitions
- Diagnosing First and Second Order Phase Transitions with Probes of Quantum Chaos
- Effects of topological and non-topological edge states on information propagation and scrambling in a Floquet spin chain
- Many-body chaos and anomalous diffusion across thermal phase transitions in two dimensions
- Information scrambling and butterfly velocity in quantum spin glass chains
- Quantum information scrambling in adiabatically-driven critical systems
- Experimental Measurement of Out-of-Time-Ordered Correlators at Finite Temperature