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Critical Phase Dualities in 1D Exactly Solvable Quasiperiodic Models.

Miguel Gonçalves1,2, Bruno Amorim3, Eduardo V Castro2,4

  • 1CeFEMA-LaPMET, Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, 1049-001 Lisboa, Portugal.

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We introduce a new class of solvable 1D quasiperiodic models with extended, localized, and critical phases. These models exhibit multifractal properties and can be experimentally realized in optical lattices.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Materials Science

Background:

  • Quasiperiodic systems exhibit complex behaviors, including localization and critical phases.
  • Understanding phase transitions and mobility edges in these systems is crucial.
  • Previous models like Aubry-André and Ganeshan et al. have provided insights but have limitations.

Purpose of the Study:

  • To propose a new, solvable class of 1D quasiperiodic tight-binding models.
  • To encompass extended, localized, and critical phases with nontrivial mobility edges.
  • To extend localized-delocalized duality transformations into multifractal critical phases.

Main Methods:

  • Analytical treatment using a novel renormalization group fixed-point approach.
  • Identification of models as fixed points of a recently proposed renormalization group procedure.
  • Exploration of localized-delocalized duality transformations.

Main Results:

  • A solvable class of 1D quasiperiodic tight-binding models is proposed.
  • The models include extended, localized, and critical phases separated by mobility edges.
  • Multifractal duality is confirmed experimentally, extending to critical phases.

Conclusions:

  • The proposed models offer a unified framework for studying quasiperiodic systems.
  • Experimental realization in optical lattices allows stabilization of multifractal phases and mobility edges without unbounded potentials.
  • This work advances the understanding and experimental control of complex quantum phases in quasiperiodic structures.