Critical state generators from perturbed flatbands

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Materials Science

Background:

• One-dimensional all-bands-flat lattices feature flat and degenerate energy bands.
• These lattices are diagonalizable via local unitary transformations.
• Previous work showed quasiperiodic perturbations induce critical-to-insulator transitions and fractality edges in specific models.

Purpose of the Study:

• Generalize findings on quasiperiodic perturbations to the entire manifold of all-bands-flat models.
• Investigate the impact of quasiperiodic perturbations across this manifold.
• Characterize the resulting critical phenomena and localization properties.

Main Methods:

• Derivation of an effective Hamiltonian for weak quasiperiodic perturbations.
• Analysis of the mapping of effective models to extended or off-diagonal Harper models.
• Study of spectral properties and transitions under varying perturbation strengths.

Main Results:

• Identification of manifold parameters leading to critical states via extended Harper models.
• Observation of localized spectra for other parameter values.
• Emergence of energy-dependent fractality edges (perturbation-independent) in the extended Harper model.
• Tunable critical-to-insulator transitions at finite disorder for the off-diagonal Harper model.

Conclusions:

• Quasiperiodic perturbations on all-bands-flat lattices lead to diverse critical behaviors and localization.
• Fractality edges are a robust feature, independent of perturbation strength in certain regimes.
• The study provides a comprehensive understanding of critical phenomena in a broad class of flat band systems.