On the relation between the magnitude and exponent of OTOCs

Abstract

We derive an identity relating the growth exponent of early-time OTOCs, the pre-exponential factor, and a third number called "branching time". The latter is defined within the dynamical mean-field framework, namely, in terms of the retarded kernel. This identity can be used to calculate stringy effects in the SYK and similar models, we also explicitly define "strings" in this context. As another application, we consider an SYK chain. If the coupling strength $\beta J$ is above a certain threshold and nonlinear (in the magnitude of OTOCs) effects are ignored, the exponent in the butterfly wavefront is exactly $2\pi /\beta$.

arXiv comment20 pages, 7 figures

References in corpus (8)

• A bound on chaos
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
• Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
• Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
• More on Supersymmetric and 2d Analogs of the SYK Model
• Universal Diffusion in Incoherent Black Holes

Cited by in corpus (51)

• Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids
• Many-Body Chaos in the Sachdev-Ye-Kitaev Model
• Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial
• A two-way approach to out-of-time-order correlators
• A symmetry algebra in double-scaled SYK
• Many-body quantum teleportation via operator spreading in the traversable wormhole protocol
• Chaos in the butterfly cone
• Operator size at finite temperature and Planckian bounds on quantum dynamics
• Transport and chaos in lattice Sachdev-Ye-Kitaev models
• Gravitational orbits, double-twist mirage, and many-body scars
• On systems of maximal quantum chaos
• Diagnosing quantum chaos in many-body systems using entanglement as a resource
• Regularization dependence of the OTOC. Which Lyapunov spectrum is the physical one?
• Pole skipping away from maximal chaos
• Many-body quantum dynamics slows down at low density
• Dirac Fast Scramblers
• Firewalls vs. Scrambling
• The Generalized OTOC from Supersymmetric Quantum Mechanics: Study of Random Fluctuations from Eigenstate Representation of Correlation Functions
• Dynamical Transition of Operator Size Growth in Quantum Systems Embedded in an Environment
• Scrambling and Lyapunov Exponent in Unitary Networks with Tunable Interactions
• Quantum bounds and fluctuation-dissipation relations
• The chiral SYK model
• A Traversable Wormhole Teleportation Protocol in the SYK Model
• Maximal quantum chaos of the critical Fermi surface
• Subleading Bounds on Chaos
• An obstacle to sub-AdS holography for SYK-like models
• Out-of-time-order correlators and Lyapunov exponents in sparse SYK
• Dynamical transition from localized to uniform scrambling in locally hyperbolic systems
• Chiral Algebras of Two-Dimensional SYK Models
• Effective description of sub-maximal chaos: stringy effects for SYK scrambling
• Operator Size Distribution in Large $N$ Quantum Mechanics of Majorana Fermions
• An Inelastic Bound on Chaos
• Mixing and localisation in random time-periodic quantum circuits of Clifford unitaries
• Space-Time Duality between Quantum Chaos and Non-Hermitian Boundary Effect
• Chiral Sachdev-Ye model: Integrability and chaos of anyons in 1+1d
• Operator size growth in Lindbladian SYK
• Strange metal phase of disordered magic-angle twisted bilayer graphene at low temperatures: from flatbands to weakly coupled Sachdev-Ye-Kitaev bundles
• Emergence of a Renormalized $1/N$ Expansion in Quenched Critical Many-Body Systems
• True SYK or (con)sequences
• Error-resilient Reversal of Quantum Chaotic Dynamics Enabled by Scramblons
• Many-body chaos in the antiferromagnetic quantum critical metal
• Phase space holography with no strings attached
• SYK does not Transit Gloria Mundi just yet
• Size Winding Mechanism beyond Maximal Chaos
• Lyapunov exponents in a Sachdev-Ye-Kitaev-type model with population imbalance in the conformal limit and beyond
• Information scrambling and butterfly velocity in quantum spin glass chains
• Hybrid Brownian SYK-Hubbard Model: from Spectral Function to Quantum Chaos
• Krylov Winding and Emergent Coherence in Operator Growth Dynamics
• Quasiparticle tunnelling in two coupled chiral SYK model
• Near-Equilibrium Approach to Transport in Complex Sachdev-Ye-Kitaev Models
• Wormholes and out-of-time ordered correlators in gauge/gravity duality