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Exact mobility edges in quasiperiodic systems without self-duality.

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We found that the relative phase in quasiperiodic potentials controls exact mobility edges (MEs) in quantum systems. These exact MEs are surprisingly robust against shifts in the potential, offering new insights into localization physics.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Disordered Systems

Background:

  • The mobility edge (ME) is crucial for understanding localization phenomena, separating localized and extended states.
  • Exact MEs are rare and sensitive to perturbations, limiting theoretical and experimental exploration.

Purpose of the Study:

  • To generalize the Aubry-André-Harper model by introducing a relative phase.
  • To analytically determine the exact mobility edge and localization lengths.
  • To investigate the impact of the relative phase and potential shifts on MEs.

Main Methods:

  • Generalization of the Aubry-André-Harper model.
  • Application of Avila's global theory for analytical computation.
  • Numerical simulations for verification.

Main Results:

  • The exact ME and localization lengths are shown to depend significantly on the relative phase.
  • The introduction of a relative phase breaks the self-duality, creating a series of MEs.
  • Exact MEs are invariant to shifts in the quasiperiodic potential, contrary to expectations.

Conclusions:

  • The relative phase offers a new control parameter for engineering exact mobility edges.
  • The robustness of exact MEs against potential shifts provides a deeper understanding of localization.
  • The study establishes a connection between exact MEs and dual models with long-range hoppings.