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Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. When two variables are correlated, it simply means that as one variable changes, so does the other. We can measure correlation by calculating a statistic known as a correlation coefficient. A correlation coefficient is a number from -1 to +1 that indicates the strength and direction of the relationship between...
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Eigenstate Correlations, Thermalization, and the Butterfly Effect.

Amos Chan1, Andrea De Luca1, J T Chalker1

  • 1Theoretical Physics, Oxford University, Parks Road, Oxford OX1 3PU, United Kingdom.

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|July 9, 2019
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Summary
This summary is machine-generated.

We reveal new correlations in quantum systems beyond the standard Eigenstate Thermalization Hypothesis (ETH). These findings, observed in Floquet systems, explain quantum scrambling and the butterfly effect with numerical evidence.

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Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Condensed matter physics

Background:

  • The Eigenstate Thermalization Hypothesis (ETH) describes thermal properties of many-body quantum systems.
  • Quantum scrambling and the butterfly effect suggest deviations from standard ETH predictions.

Purpose of the Study:

  • To investigate eigenstate correlations in ergodic, spatially extended many-body quantum systems.
  • To identify and characterize universal structures in quantum systems that go beyond ETH.
  • To explore these phenomena in the context of Floquet systems.

Main Methods:

  • Analysis of statistical properties of matrix elements of local observables.
  • Theoretical determination of universal correlation forms for Floquet systems.
  • Numerical simulations of a Floquet quantum circuit.

Main Results:

  • Demonstrated that ETH accurately describes many eigenstate correlations.
  • Identified additional correlations beyond ETH, particularly at long distances and small eigenvalue separations in Floquet systems.
  • Numerical studies confirmed both the accuracy of ETH and the existence of predicted additional correlations.

Conclusions:

  • The study refines our understanding of quantum chaos and thermalization in many-body systems.
  • The identified correlations provide new insights into quantum scrambling and the butterfly effect.
  • The findings are crucial for understanding the behavior of complex quantum systems, especially those with periodic driving (Floquet systems).