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This study explores quantum systems, revealing a Janus-type transition where eigenstates shift from delocalized to localized. Some measures align with random matrix theory, while others show unique, nonuniversal behavior in entanglement entropy.

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics

Background:

  • Delocalized to localized eigenstate transitions are well-studied in quadratic and interacting models.
  • The delocalized regime typically shows diffusion and quantum chaos, aligning with random matrix theory (RMT).
  • However, some quadratic models exhibit delocalization without single-particle quantum chaos.

Purpose of the Study:

  • Investigate eigenstate transitions in one-dimensional Anderson and Wannier-Stark models.
  • Analyze behavior in a nonstandard thermodynamic limit involving system-size-dependent parameter rescaling.
  • Characterize the nature of the transition point, particularly its potential Janus-type properties.

Main Methods:

  • Study of one-dimensional Anderson and Wannier-Stark models.
  • Analysis in a nonstandard thermodynamic limit with rescaled parameters.
  • Examination of eigenstate properties, including entanglement entropies and their dependence on bipartition.

Main Results:

  • Observed eigenstate transitions from quasimomentum space localization (ballistic transport) to position space localization (no transport).
  • Identified a Janus-type transition point where some measures suggest RMT-like universality, while others deviate.
  • Demonstrated diverse volume-law behaviors in eigenstate entanglement entropies, with coefficients varying from universal to nonuniversal values.

Conclusions:

  • Quadratic systems can exhibit complex eigenstate transitions beyond simple RMT predictions.
  • The Janus-type transition highlights a nuanced interplay between universality and nonuniversality.
  • Eigenstate entanglement entropy in quadratic systems displays a rich diversity, even in non-maximally entangled states.