Numerical Investigation of Localization in Two-Dimensional Quasiperiodic Mosaic Lattice

TL;DR

This paper extends a one-dimensional quasiperiodic lattice model to two dimensions, studying its localization properties through numerical methods and revealing both similarities and differences with disordered systems.

Contribution

The paper introduces a two-dimensional quasiperiodic mosaic lattice model and analyzes its localization phase diagram and conductance properties numerically.

Findings

Presence of mobility edges in the 2D model

Similarities to 3D disordered systems in conductance behavior

Distinct localization characteristics compared to disordered systems

Abstract

A one-dimensional lattice model with mosaic quasiperiodic potential is found to exhibit interesting localization properties, e.g., clear mobility edges [Y. Wang et al., Phys. Rev. Lett. \textbf{125}, 196604 (2020)]. We generalize this mosaic quasiperiodic model to a two-dimensional version, and numerically investigate its localization properties: the phase diagram from the fractal dimension of the wavefunction, the statistical and scaling properties of the conductance. Compared with disordered systems, our model shares many common features but also exhibits some different characteristics in the same dimensionality and the same universality class. For example, the sharp peak at $g\sim 0$ of the critical distribution and the large $g$ limit of the universal scaling function $\beta$ resemble those behaviors of three-dimensional disordered systems.