Quantum operator growth bounds for kicked tops and semiclassical spin chains

Abstract

We present a framework for understanding the dynamics of operator size, and bounding the growth of out-of-time-ordered correlators, in models of large-$S$ spins. Focusing on the dynamics of a single spin, we show the finiteness of the Lyapunov exponent in the large-$S$ limit; our bounds are tighter than the best known Lieb-Robinson-type bounds on these systems. We numerically find our upper bound on Lyapunov exponents is within an order of magnitude of numerically computed values in classical and quantum kicked top models. Generalizing our results to coupled large-$S$ spins on lattices, we show that the butterfly velocity, which characterizes the spatial speed of quantum information scrambling, is finite as $S\to \infty$. We emphasize qualitative differences between operator growth in semiclassical large-spin models, and quantum holographic systems including the Sachdev-Ye-Kitaev model.

arXiv comment7+3 pages, 2 figures. v2: modified/improved Lieb-Robinson and quantum walk bounds. v3: published version

References in corpus (47)

• A bound on chaos
• Black holes and the butterfly effect
• Operator Spreading in Random Unitary Circuits
• Localized shocks
• Spectral Gap and Exponential Decay of Correlations
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
• Does scrambling equal chaos?
• Divergence of the Classical trajectories and Weak Localization
• Unifying fast scrambling, thermalization and entanglement through the measurement of FOTOCs in the Dicke model
• Scrambling and entanglement spreading in long-range spin chains
• Many-body chaos at weak coupling
• Operator growth in the SYK model
• Quantum chaos on a critical Fermi surface
• Quantum Epidemiology: Operator Growth, Thermal Effects, and SYK
• Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems
• Approximating the Sachdev-Ye-Kitaev model with Majorana wires
• Quantum holography in a graphene flake with an irregular boundary
• Strictly linear light cones in long-range interacting systems of arbitrary dimensions
• Bridging entanglement dynamics and chaos in semiclassical systems
• Digital Quantum Simulation, Trotter Errors, and Quantum Chaos of the Kicked Top
• Entanglement rates and area laws
• Shot noise in chaotic systems: "classical" to quantum crossover
• Hierarchy of linear light cones with long-range interactions
• Spin squeezing with short-range spin-exchange interactions
• Treelike interactions and fast scrambling with cold atoms
• Light-cone spreading of perturbations and the butterfly effect in a classical spin chain
• Fast scrambling on sparse graphs
• Minimal Model for Fast Scrambling
• Tightening the Lieb-Robinson Bound in Locally-Interacting Systems
• A cavity-QED simulator of slow and fast scrambling
• Scrambling in the Dicke model
• Integrable and chaotic dynamics of spins coupled to an optical cavity
• Chaos in a classical limit of the Sachdev-Ye-Kitaev model
• Lieb-Robinson bounds for spin-boson lattice models and trapped ions
• On operator growth and emergent Poincaré symmetries
• Why do Things Fall?
• Fast scrambling without appealing to holographic duality
• Many-body quantum dynamics slows down at low density
• Bound on quantum scrambling with all-to-all interactions
• Quantum echo dynamics in the Sherrington-Kirkpatrick model
• Quantum Scrambling and State Dependence of the Butterfly Velocity
• Non-perturbative dynamics of the operator size distribution in the Sachdev-Ye-Kitaev model
• Size of bulk fermions in the SYK model
• The Weyl-Wigner-Moyal Formalism for Spin
• Operator growth bounds in a cartoon matrix model
• Operator Size for Holographic Field Theories

Cited by in corpus (21)

• Krylov complexity in saddle-dominated scrambling
• Operator growth in 2d CFT
• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Spread Complexity and Topological Transitions in the Kitaev Chain
• Speed limits and locality in many-body quantum dynamics
• Classical many-body chaos with and without quasiparticles
• Spread complexity in saddle-dominated scrambling
• Spread complexity as classical dilaton solutions
• Finite speed of quantum information in models of interacting bosons at finite density
• Dynamical Transition of Operator Size Growth in Quantum Systems Embedded in an Environment
• Scrambling and quantum chaos indicators from long-time properties of operator distributions
• Optimal Frobenius light cone in spin chains with power-law interactions
• Operator Size Distribution in Large $N$ Quantum Mechanics of Majorana Fermions
• Quantum Chaos and Circuit Parameter Optimization
• Analyticity constraints bound the decay of the spectral form factor
• Out-of-Time-Order-Correlator for van der Waals potential
• Free Probability approach to spectral and operator statistics in Rosenzweig-Porter random matrix ensembles
• Scrambling Transition in Free Fermion Systems Induced by a Single Impurity
• Periodicity of dynamical signatures of chaos in quantum kicked top
• Information scrambling of the dilute Bose gas at low temperature
• Out-of-time-order correlators of nonlocal block-spin and random observables in integrable and nonintegrable spin chains