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We reveal how out-of-time-order correlators (OTOCs) dynamically detect quantum phase transitions. This method clarifies key ingredients for identifying quantum phases and validates existing numerical findings.

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Area of Science:

  • Quantum Information Science
  • Condensed Matter Physics

Background:

  • Out-of-time-order correlators (OTOCs) are sensitive probes of quantum chaos and entanglement.
  • Understanding the relationship between OTOCs and quantum phase transitions (QPTs) is crucial for characterizing complex quantum systems.

Purpose of the Study:

  • To elucidate the dynamic relationship between OTOCs and QPTs.
  • To develop a general analytical method for detecting quantum phases using OTOCs.
  • To provide a theoretical framework explaining existing numerical observations.

Main Methods:

  • Analytical study of OTOC dynamics in a degenerate spectrum.
  • Investigating the behavior of OTOCs across different quantum phases.
  • Application of the developed method to the critical XXZ model.

Main Results:

  • Established a clear connection between OTOC dynamics and quantum phase transitions.
  • Identified key features of OTOCs that signal different quantum phases.
  • The analytical method successfully explains and reproduces numerical results in the literature.
  • Predictions were numerically confirmed using the XXZ model.

Conclusions:

  • OTOCs offer a powerful tool for dynamically detecting and characterizing quantum phases.
  • The developed analytical framework provides a universal approach for studying OTOCs in QPTs.
  • This work bridges theoretical insights and numerical validations in the study of quantum dynamics.