Critical-to-Insulator Transitions and Fractality Edges in Perturbed Flatbands

TL;DR

This paper investigates how quasiperiodic perturbations affect one-dimensional flatband models, revealing energy-dependent transitions between localized, critical, and insulating states, and identifying fractality edges that separate these phases.

Contribution

It introduces a detailed analysis of critical-to-insulator transitions and fractality edges in perturbed flatband systems, highlighting the energy dependence of these transitions.

Findings

Identification of localized and critical states under quasiperiodic perturbations.

Discovery of energy-dependent critical-to-insulator transitions.

Observation of fractality edges separating different electronic phases.

Abstract

We study the effect of quasiperiodic perturbations on one-dimensional all-bands-flat lattice models. Such networks can be diagonalized by a finite sequence of local unitary transformations parameterized by angles $\theta_i$. Without loss of generality, we focus on the case of two bands with bandgap $\Delta$. Weak perturbations lead to an effective Hamiltonian with both on- and off-diagonal quasiperiodic terms that depend on $\theta_i$. For some angle values, the effective model coincides with the extended Harper model. By varying the parameters of the quasiperiodic potentials, \iffalse and the manifold angles $\theta_i$ \fi we observe localized insulating states and an entire parameter range hosting critical states with subdiffusive transport. For finite quasiperiodic potential strength, the critical-to-insulating transition becomes energy dependent with what we term fractality edges separating localized from critical states.