Out-of-time-order correlator computation based on discrete truncated Wigner approximation

Abstract

We propose a method based on the discrete truncated Wigner approximation (DTWA) for computing out-of-time-order correlators. This method is applied to long-range interacting quantum spin systems where the interactions decay as a power law with distance. As a demonstration, we use a squared commutator of local operators and its higher-order extensions that describe quantum information scrambling under Hamilton dynamics. Our results reveal that the DTWA method accurately reproduces the exact dynamics of the average spreading of quantum information (i.e., the squared commutator) across all time regimes in strongly long-range interacting systems. We also identify limitations in the DTWA method when capturing dynamics in weakly long-range interacting systems and the fastest spreading of quantum information. Then we apply the DTWA method to investigate the system-size dependence of the scrambling time in strongly long-range interacting systems. We reveal that the scaling behavior of the scrambling time for large system sizes qualitatively changes depending on the interaction range. This work provides and demonstrates a new technique to study scrambling dynamics in long-range interacting quantum spin systems.

11 pages, 4 captioned figures

References in corpus (23)

• A bound on chaos
• Black holes and the butterfly effect
• Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
• Phase space representation of quantum dynamics
• Chaos and complexity by design
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• Measuring out-of-time-order correlators on a nuclear magnetic resonance quantum simulator
• A Universal Operator Growth Hypothesis
• Long-range interacting quantum systems
• Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space
• Probing quantum information propagation with out-of-time-ordered correlators
• Schwinger-Keldysh formalism I: BRST symmetries and superspace
• Hierarchy of linear light cones with long-range interactions
• Fast scrambling on sparse graphs
• Absence of fast scrambling in thermodynamically stable long-range interacting systems
• Verifying the upper bound on the speed of scrambling with the analogue Hawking radiation of trapped ions
• Transport and entanglement growth in long-range random Clifford circuits
• Bound on quantum scrambling with all-to-all interactions
• Prethermalization in the transverse-field Ising chain with long-range interactions
• Lieb Robinson bounds and out of time order correlators in a long range spin chain
• Out-of-time-order fluctuation-dissipation theorem
• Surprises in the Deep Hilbert Space of all-to-all systems: From super-exponential scrambling to slow entanglement growth
• Performance evaluation of the discrete truncated Wigner approximation for quench dynamics of quantum spin systems with long-range interactions