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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Materials Science

Background:

  • Exact solutions for mobility edges (MEs) in one-dimensional quasiperiodic systems are scarce.
  • Existing methods like self-duality theory and renormalization groups have limitations.
  • The mosaic model was previously misunderstood regarding its ME origins.

Purpose of the Study:

  • To uncover new physical models with exactly solvable mobility edges (MEs).
  • To investigate the role of hidden self-duality in quasiperiodic network models.
  • To provide a framework for understanding and predicting MEs in diverse systems.

Main Methods:

  • Analyzing quasiperiodic network models with periodic and quasiperiodic sites.
  • Deriving effective Hamiltonians by integrating out periodic sites.
  • Applying the concept of hidden self-duality to identify exact MEs.
  • Introducing resonant states to analyze ME characteristics.

Main Results:

  • A class of quasiperiodic network models exhibits hidden self-duality in their effective Hamiltonians.
  • This hidden self-duality leads to exact solutions for mobility edges (MEs).
  • The mosaic model's MEs arise from this previously unrecognized self-duality.
  • A method to determine MEs in various models, including non-Hermitian ones, is established.

Conclusions:

  • Hidden self-duality is a key mechanism for realizing exact MEs in quasiperiodic systems.
  • The findings offer a new perspective on Anderson transitions and localization phenomena.
  • Experimental verification using optical and acoustic waveguide arrays is feasible.