Mixed spectra and partially extended states in a two-dimensional quasiperiodic model

TL;DR

This paper introduces a 2D quasiperiodic model with complex localization properties, including partially extended states on low-disorder lines, leading to mixed spectra and unique transport phenomena.

Contribution

It presents a 2D generalization of the Aubry-André model revealing complex localization behavior and spatially separated extended and localized states, which was not known before.

Findings

Partially extended states appear on low-disorder lines.

No mobility edge; localized and extended states coexist.

Ballistic transport occurs along low-disorder lines.

Abstract

We introduce a two-dimensional generalisation of the quasiperiodic Aubry-Andr\'e model. Even though this model exhibits the same duality relation as the one-dimensional version, its localisation properties are found to be substantially more complex. In particular, partially extended single-particle states appear for arbitrarily strong quasiperiodic modulation. They are concentrated on a network of low-disorder lattice lines, while the rest of the lattice hosts localised states. This spatial separation protects the localised states from delocalisation, so no mobility edge emerges in the spectrum. Instead, localised and partially extended states are interspersed, giving rise to an unusual type of mixed spectrum and enabling complex dynamics even in the absence of interactions. A striking example is ballistic transport across the low-disorder lines while the rest of the system remains localised. This behaviour is robust against disorder and other weak perturbations. Our model is thus directly amenable to experimental studies and promises fascinating many-body localisation properties.