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Identifying Quantum Many-Body Integrability and Chaos Using Eigenstate Trace Distances.

Reyhaneh Khasseh1, Jiaju Zhang2, Markus Heyl1

  • 1Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg, D-86135 Augsburg, Germany.

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This summary is machine-generated.

Researchers introduce a new indicator for quantum many-body integrability and chaos using eigenstate statistics. This method offers a more faithful classification of quantum systems, addressing limitations of existing indicators.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Statistical mechanics

Background:

  • Defining quantum many-body integrability and chaos is crucial for understanding quantum matter.
  • Existing indicators, like level-spacing statistics, have limitations in classifying complex quantum systems.
  • The quantum many-body kicked top serves as a test case where traditional methods show discrepancies.

Purpose of the Study:

  • To introduce and validate a novel indicator for quantum many-body integrability and chaos.
  • To provide a more reliable method for classifying quantum systems.
  • To address the limitations of current indicators, particularly in specific model systems.

Main Methods:

  • Developing a new indicator based on the statistics of eigenstates.
  • Utilizing nearest-neighbor subsystem trace distances for classification.
  • Conducting extensive numerical simulations across diverse model systems.

Main Results:

  • The new indicator, based on nearest-neighbor trace distances, provides a faithful classification of quantum integrability and chaos.
  • Demonstrated effectiveness across various systems: random matrix theories, free fermions, Bethe-ansatz systems, and many-body localization models.
  • Successfully reclassified the quantum many-body kicked top, aligning with its known exact solvability.

Conclusions:

  • Nearest-neighbor subsystem trace distances offer a robust and alternative indicator for quantum many-body integrability and chaos.
  • This new indicator overcomes limitations of traditional methods, particularly for systems like the quantum many-body kicked top.
  • The indicator shows potential applicability to other areas, including the study of the many-body localization transition.