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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Statistical mechanics

Background:

  • Characterizing quantum phase transitions in highly excited Hamiltonian eigenstates remains a significant challenge.
  • Developing time-domain tools for analyzing these transitions is crucial for advancing quantum mechanics understanding.

Purpose of the Study:

  • To introduce and demonstrate a novel method for characterizing quantum phase transitions in the time domain.
  • To explore the applicability of this method across different types of quantum systems, including both quadratic and interacting models.

Main Methods:

  • Analysis of scaled survival probability, with time normalized by the Heisenberg time.
  • Application of the method to paradigmatic quadratic models: the one-dimensional Aubry-Andre model and the three-dimensional Anderson model.
  • Extension of the analysis to the interacting avalanche model, a system exhibiting ergodicity breaking phase transitions.

Main Results:

  • A scale-invariant behavior of scaled survival probability was observed at eigenstate transitions in quadratic models.
  • Similar scale-invariant phenomenology was surprisingly found in the interacting avalanche model.
  • This indicates an unexpected connection between localization transitions in quadratic systems and ergodicity breaking in interacting systems.

Conclusions:

  • Scaled survival probability serves as a powerful, universal tool for identifying quantum phase transitions in the time domain.
  • The study reveals a profound similarity between localization and ergodicity breaking phase transitions, bridging distinct areas of quantum physics.
  • This finding opens new avenues for theoretical and experimental investigations into complex quantum phenomena.