Quasi-periodic flat-band model constructed by molecular-orbital representation

TL;DR

This paper introduces a quasi-periodic tight-binding model with flat-band zero-energy modes, analyzing its particle density distribution, hyperuniformity, and mode localization transition, extending the understanding of quasi-periodic systems.

Contribution

The paper constructs a novel quasi-periodic flat-band model using molecular-orbital representation, revealing unique density and localization properties.

Findings

Particle density shows sublattice dependence.

Density distribution is class-I hyperuniform.

Finite-energy modes undergo extended-to-localized transition.

Abstract

We construct a tight-binding model that hosts both a quasi-periodic nature and marcoscopically-dengenerate zero-energy modes. The model can be regarded as a counterpart of the Aubry-Andr\'{e}-Harper (AAH) model, which is a paradigmatic example of the quasi-periodic tight-binding model. Our main focus is on the many-body state where the flat-band-like degenerate zero-energy modes are fully occupied. We find a characteristic sublattice dependence of the particle density distribution. Further, by analyzing the hyperuniformity of the particle density distribution, we find that it belongs to the class-I hyperuniform distribution, regardless of the model parameter. We also show that, upon changing the parameter, the finite-energy modes exhibit the same extended-to-localized transition as that for the original AAH model.