Critical Phase Dualities in 1D Exactly Solvable Quasiperiodic Models

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.