Fractional Statistics and the Butterfly Effect
arXiv:1602.06543 · doi:10.1007/JHEP08(2016)129
Abstract
Fractional statistics and quantum chaos are both phenomena associated with the non-local storage of quantum information. In this article, we point out a connection between the butterfly effect in (1+1)-dimensional rational conformal field theories and fractional statistics in (2+1)-dimensional topologically ordered states. This connection comes from the characterization of the butterfly effect by the out-of-time-order-correlator proposed recently. We show that the late-time behavior of such correlators is determined by universal properties of the rational conformal field theory such as the modular S-matrix and conformal spins. Using the bulk-boundary correspondence between rational conformal field theories and (2+1)-dimensional topologically ordered states, we show that the late time behavior of out-of-time-order-correlators is intrinsically connected with fractional statistics in the topological order. We also propose a quantitative measure of chaos in a rational conformal field theory, which turns out to be determined by the topological entanglement entropy of the corresponding topological order.
Published version, 1+25 pages, 10 figures
References in corpus (5)
- Non-Abelian Anyons and Topological Quantum Computation
- Black holes as mirrors: quantum information in random subsystems
- Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
- Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
- Decoherence of Anyonic Charge in Interferometry Measurements
Cited by in corpus (40)
- Chaos and complexity by design
- Out-of-Time-Order Correlation for Many-Body Localization
- Velocity-dependent Lyapunov exponents in many-body quantum, semi-classical, and classical chaos
- Bounding the Space of Holographic CFTs with Chaos
- Clean Floquet Time Crystals: Models and Realizations in Cold Atoms
- Quantum Chaos and Holographic Tensor Models
- Out-of-Time-Order Correlation at a Quantum Phase Transition
- Three Dimensional View of the SYK/AdS Duality
- Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath
- On CFT and Quantum Chaos
- Light Cone Bootstrap in General 2D CFTs and Entanglement from Light Cone Singularity
- Probing excited-state quantum phase transition in a quantum many body system via out-of-time-ordered correlator
- Three Dimensional View of Arbitrary SYK models
- Out-of-Time-Order Correlation in Marginal Many-Body Localized Systems
- Entanglement Entropy, OTOC and Bootstrap in 2D CFTs from Regge and Light Cone Limits of Multi-point Conformal Block
- Nonlinear sigma model approach to many-body quantum chaos: Regularized and unregularized out-of-time-ordered correlators
- Conformal field theory and the web of quantum chaos diagnostics
- Entanglement Features of Random Hamiltonian Dynamics
- Lorentzian Dynamics and Factorization Beyond Rationality
- Renyi Entropy for Local Quenches in 2D CFTs from Numerical Conformal Blocks
- Signature of quantum chaos in operator entanglement in 2d CFTs
- Entanglement of Local Operators and the Butterfly Effect
- Out-of-time-ordered correlators in short-range and long-range hard-core boson models and in the Luttinger-liquid model
- Scattering effect on entanglement propagation in RCFTs
- Entanglement entropy in (1+1)D CFTs with multiple local excitations
- Out-of-Time-Order correlators in driven conformal field theories
- New Properties of Large- Conformal Blocks from Recursion Relation
- Evolution of Entanglement Entropy in Orbifold CFTs
- Out-of-Time-Ordered Correlators in
- Out-of-Time-Order Correlation as a Witness for Topological Phase Transitions
- Butterflies from Information Metric
- Localization of Extended Quantum Objects
- Characteristic, dynamic, and near saturation regions of Out-of-time-order correlation in Floquet Ising models
- Exact Dynamical Correlations of Hard-Core Anyons in One-Dimensional Lattices
- Asymmetric butterfly velocities in 2-local Hamiltonians
- Floquet engineered inhomogeneous quantum chaos in critical systems
- Entanglement wedge method, out-of-time-ordered correlators, and pole skipping
- Scrambling in the Quantum Lifshitz Model
- Out-of-time-order correlation and detection of phase structure in Floquet transverse Ising spin system
- Out-of-time-order correlators of nonlocal block-spin and random observables in integrable and nonintegrable spin chains