The operator Lévy flight: light cones in chaotic long-range interacting systems

Abstract

We argue that chaotic power-law interacting systems have emergent limits on information propagation, analogous to relativistic light cones, which depend on the spatial dimension $d$ and the exponent $\alpha$ governing the decay of interactions. Using the dephasing nature of quantum chaos, we map the problem to a stochastic model with a known phase diagram. A linear light cone results for $\alpha \ge d+1/2$. We also provide a Lévy flight (long-range random walk) interpretation of the results and show consistent numerical data for 1d long-range spin models with 200 sites.

arXiv commentpublished version: improved presentation of the scaling analysis around Tab. I, additional data in Fig. 3

References in corpus (49)

• A bound on chaos
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Observation of discrete time-crystalline order in a disordered dipolar many-body system
• Quantum many-body scars
• Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
• Realizing a lattice spin model with polar molecules
• Effective quantum spin systems with ion traps
• Time-dependent variational principle for quantum lattices
• Unifying time evolution and optimization with matrix product states
• Operator Spreading in Random Unitary Circuits
• Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
• Spectral Gap and Exponential Decay of Correlations
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
• Measuring the scrambling of quantum information
• Emergence and Frustration of Magnetic Order with Variable-Range Interactions in a Trapped Ion Quantum Simulator
• Towards the fast scrambling conjecture
• Measuring out-of-time-order correlators on a nuclear magnetic resonance quantum simulator
• Verified Quantum Information Scrambling
• Spread of correlations in long-range interacting quantum systems
• Time-evolving a matrix product state with long-ranged interactions
• Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation
• Exploring Localization in Nuclear Spin Chains
• Entanglement entropy for the long range Ising chain
• Nearly-linear light cones in long-range interacting quantum systems
• Operator growth in the SYK model
• Dynamical phase diagram of spin chains with long-range interactions
• Velocity-dependent Lyapunov exponents in many-body quantum, semi-classical, and classical chaos
• Measurement of many-body chaos using a quantum clock
• Jarzynski-like equality for the out-of-time-ordered correlator
• Real-time Dynamics in U(1) Lattice Gauge Theories with Tensor Networks
• The quasiprobability behind the out-of-time-ordered correlator
• The acceleration of evolutionary spread by long-range dispersal
• Finite speed of quantum scrambling with long range interactions
• Perfect state transfer in long-range interacting spin chains
• Locality, Quantum Fluctuations, and Scrambling
• Thermodynamics of quantum information scrambling
• Accessing scrambling using matrix product operators
• Quantum thermalization dynamics with Matrix-Product States
• Locality and digital quantum simulation of power-law interactions
• Emergent perturbation independent decay of the Loschmidt echo in a many-spin system studied through scaled dipolar dynamics
• Efficient decoding for the Hayden-Preskill protocol
• Fast State Transfer and Entanglement Renormalization Using Long-Range Interactions
• Operator Dynamics in Brownian Quantum Circuit
• Exploring quantum signatures of chaos on a Floquet synthetic lattice
• Quantum chaos dynamics in long-range power law interaction systems
• Quantum Communication in Spin Systems With Long-Range Interactions
• Emergent locality in systems with power-law interactions
• Generalized Central Limit Theorem and Renormalization Group

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• Quantum information scrambling in a trapped-ion quantum simulator with tunable range interactions
• Fate of measurement-induced phase transition in long-range interactions
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• Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial
• Hierarchy of linear light cones with long-range interactions
• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Many-body quantum teleportation via operator spreading in the traversable wormhole protocol
• Absence of fast scrambling in thermodynamically stable long-range interacting systems
• Universal Entanglement Transitions of Free Fermions with Long-range Non-unitary Dynamics
• Parallel time-dependent variational principle algorithm for matrix product states
• Lieb-Robinson bound and almost-linear light-cone in interacting boson systems
• Transport and entanglement growth in long-range random Clifford circuits
• Many-body quantum dynamics slows down at low density
• Lieb Robinson bounds and out of time order correlators in a long range spin chain
• Optimal Frobenius light cone in spin chains with power-law interactions
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• Hydrodynamics in long-range interacting systems with center-of-mass conservation
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• Real-time correlators in chaotic quantum many-body systems
• Scaling laws of the out-of-time-order correlators at the transition to the spontaneous $\mathcal{P}\mathcal{T}$-symmetry breaking in a Floquet system
• Hydrodynamic theory of scrambling in chaotic long-range interacting systems
• Inhomogeneity induced shortcut to adiabaticity in Ising chains with long-range interactions
• Impact of dephasing on non-equilibrium steady-state transport in fermionic chains with long-range hopping
• Information Scrambling and the Correspondence of Entanglement- and Operator Dynamics in Systems with Nonlocal Interactions
• Concentration of OTOC and Lieb-Robinson velocity in random Hamiltonians
• Superdiffusive transport on lattices with nodal impurities
• The Measurement-induced Transition in Long-range Interacting Quantum Circuits
• Onset of scrambling as a dynamical transition in tunable-range quantum circuits
• Information Scrambling in Free Fermion Systems with a Sole Interaction
• Fast scrambling dynamics and many-body localization transition in an all-to-all disordered quantum spin model
• Scrambling Transition in Free Fermion Systems Induced by a Single Impurity
• Global Out of Time Order Correlators as a Signature of Scrambling Dynamics of Local Observables
• Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling
• Krylov Winding and Emergent Coherence in Operator Growth Dynamics