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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Statistical mechanics

Background:

  • Investigating the behavior of closed quantum systems under non-equilibrium conditions.
  • Understanding the interplay between disorder and interactions, crucial for phenomena like Anderson localization.
  • Exploring the concept of dynamical state-space localization as a probe for quantum system behavior.

Purpose of the Study:

  • To analyze the nonequilibrium interplay between disorder and interactions in closed quantum systems.
  • To connect real-space and state-space localization through maximally localized states (ML-states).
  • To investigate the impact of these competing mechanisms on quantum dynamics and equilibration.

Main Methods:

  • Calculation of the Loschmidt echo to quantify dynamical state-space localization.
  • Numerical simulations for both noninteracting and interacting systems.
  • Analytical evaluation in the single-particle case.
  • Analysis of gap statistics to assess effective integrability.

Main Results:

  • In noninteracting systems, the Loschmidt echo increases monotonically with disorder, inversely proportional to localization length.
  • In interacting systems, equilibration is bounded by a length scale inversely related to the ML-state echo.
  • Simultaneous presence of disorder and interactions leads to non-monotonic echo behavior, indicating a complex interplay.
  • This interplay induces delocalization in both dynamics and real-space, also reflected in gap statistics.

Conclusions:

  • Dynamical state-space localization, via Loschmidt echo, reveals a non-trivial interplay between disorder and interactions.
  • The study demonstrates how these competing localization mechanisms can lead to unexpected delocalization phenomena.
  • Findings offer insights into quantum chaos, localization-delocalization transitions, and the limits of equilibration in closed quantum systems.