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Operator growth from global out-of-time-order correlators.

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Operator growth in chaotic systems can be measured using global operators, not just local ones. This allows for easier experimental observation of quantum scrambling dynamics in many-body systems.

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Area of Science:

  • Quantum chaos
  • Many-body physics
  • Quantum information

Background:

  • Operator growth, a key indicator of quantum chaos, is typically studied using local operators and out-of-time-order correlators.
  • Diagnosing operator growth often requires complex local control and readout, limiting experimental accessibility.

Purpose of the Study:

  • To demonstrate that operator growth can be diagnosed using global operators.
  • To show that global measurements can reveal the spacetime characteristics of operator growth without local control.
  • To extend the understanding of operator growth in chaotic systems with power-law interactions.

Main Methods:

  • Theoretical analysis of operator growth in chaotic many-body systems.
  • Utilizing out-of-time-order correlators of global operators.
  • Comparison with existing experimental data from nuclear spin systems.

Main Results:

  • Operator growth leaves a distinct signature in out-of-time-order correlators of global operators.
  • Global measurements can effectively probe the spacetime shape of operator growth.
  • Existing nuclear spin data aligns well with the developed theoretical framework for power-law interactions.

Conclusions:

  • Global operators provide a viable and experimentally accessible method for diagnosing operator growth and quantum scrambling.
  • The theory predicts super-polynomial operator growth in 3D dipolar systems.
  • Future experiments with nuclear spins and ultra-cold polar molecules can potentially observe these phenomena.