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.

7+3 pages, 2 figures. v2: modified/improved Lieb-Robinson and quantum walk bounds. v3: published version

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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