Scrambling and Lyapunov Exponent in Unitary Networks with Tunable Interactions
arXiv:2009.10104 · doi:10.1103/PhysRevB.103.L121111
Abstract
Scrambling of information in a quantum many-body system, quantified by the out-of-time-ordered correlator (OTOC), is a key manifestation of quantum chaos. A regime of exponential growth in the OTOC, characterized by a Lyapunov exponent, has so far mostly been observed in systems with a high-dimensional local Hilbert space and in weakly-coupled systems. Here, we propose a general criterion for the existence of a well-defined regime of exponential growth of the OTOC in spatially extended systems with local interactions. In such systems, we show that a parametrically long period of exponential growth requires the butterfly velocity to be much larger than the Lyapunov exponent times a microscopic length scale, such as the lattice spacing. As an explicit example, we study a random unitary circuit with tunable interactions. In this model, we show that in the weakly interacting limit the above criterion is satisfied, and there is a prolonged window of exponential growth. Our results are based on numerical simulations of both Clifford and universal random circuits supported by an analytical treatment.
References in corpus (50)
- The density-matrix renormalization group in the age of matrix product states
- Chaos and Quantum Thermalization
- A bound on chaos
- Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
- Comments on the Sachdev-Ye-Kitaev model
- Black holes and the butterfly effect
- The many-body localization phase transition
- Black holes as mirrors: quantum information in random subsystems
- Operator Spreading in Random Unitary Circuits
- Chaos in quantum channels
- Quantum Entanglement Growth Under Random Unitary Dynamics
- Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
- Black Holes and Random Matrices
- Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
- Measuring the scrambling of quantum information
- Instantaneous non-local computation of low T-depth quantum circuits
- The Heisenberg Representation of Quantum Computers
- Two-dimensional conformal field theory and the butterfly effect
- A Universal Operator Growth Hypothesis
- Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
- Lieb-Robinson and the butterfly effect
- Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation
- Spectral statistics in spatially extended chaotic quantum many-body systems
- Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
- Does scrambling equal chaos?
- Many-body chaos at weak coupling
- Operator growth in the SYK model
- Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems
- Many-body quantum chaos: Analytic connection to random matrix theory
- Information propagation in isolated quantum systems
- Velocity-dependent Lyapunov exponents in many-body quantum, semi-classical, and classical chaos
- Weak Quantum Chaos
- Onset of many-body chaos in the model
- Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits
- Quantum butterfly effect in weakly interacting diffusive metals
- Scrambling in Random Unitary Circuits: Exact Results
- Locality, Quantum Fluctuations, and Scrambling
- Out-of-time-ordered density correlators in Luttinger liquids
- Decoupling with random quantum circuits
- On the relation between the magnitude and exponent of OTOCs
- Universal Spectral Correlations in the Chaotic Wave Function, and the Development of Quantum Chaos
- Transport and chaos in lattice Sachdev-Ye-Kitaev models
- Nonlinear sigma model approach to many-body quantum chaos: Regularized and unregularized out-of-time-ordered correlators
- Kinetic theory for classical and quantum many-body chaos
- Signature of quantum chaos in operator entanglement in 2d CFTs
- Operator scrambling and quantum chaos
- Coarse-grained dynamics of operator and state entanglement
- Non-perturbative dynamics of the operator size distribution in the Sachdev-Ye-Kitaev model
- Quantum circuits with classically simulable operator scrambling
- Scrambling in the Quantum Lifshitz Model
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- Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids
- Planckian Dissipation in Metals
- Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial
- Speed limits and locality in many-body quantum dynamics
- Chaos and Ergodicity in Extended Quantum Systems with Noisy Driving
- Out-of-time-order correlator in the quantum Rabi model
- Operator Growth from Global Out-of-time-order Correlators
- Emergent Symmetry in Brownian SYK Models and Charge Dependent Scrambling
- Dynamical Freezing in Exactly Solvable Models of Driven Chaotic Quantum Dots
- Charge transport, information scrambling and quantum operator-coherence in a many-body system with U(1) symmetry
- Towards the Web of Quantum Chaos Diagnostics
- Temporal fluctuations of correlators in integrable and chaotic quantum systems
- Many-body chaos and anomalous diffusion across thermal phase transitions in two dimensions
- Growth of a renormalized operator as a probe of chaos
- Fast Scrambling in Classically Simulable Quantum Circuits
- Fluctuation-stable generalized entropy probes of spectral heterogeneity