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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Chaos theory

Background:

  • Characterizing quantum many-body chaos is crucial for understanding complex quantum systems.
  • Traditional methods like out-of-time-ordered correlators (OTOCs) may not capture chaos in all systems, especially locally interacting ones.
  • Random matrix theory (RMT) provides a powerful framework for describing complex spectra.

Purpose of the Study:

  • To propose a novel characterization of quantum many-body chaos.
  • To develop a method applicable to systems that do not exhibit exponential Lyapunov growth in OTOCs.
  • To connect operator correlations to spectral properties resembling random matrix theory.

Main Methods:

  • Organizing pair correlations of simple operators into a matrix.
  • Analyzing the spectrum of this correlation matrix.
  • Numerical simulations of the Sachdev-Ye-Kitaev (SYK) model and the one-dimensional XXZ spin chain with a random magnetic field.

Main Results:

  • The correlation matrices exhibit spectra characteristic of random matrix theory.
  • This characterization is effective for locally interacting systems.
  • Numerical studies confirm the validity of the proposed method in both the SYK and XXZ models.

Conclusions:

  • The proposed operator correlation matrix provides a robust tool for characterizing quantum chaos.
  • This method offers insights into the spectral properties of many-body quantum systems.
  • It extends the study of quantum chaos to systems where traditional OTOC measures are less informative.