Anderson localization transitions with and without random potentials

TL;DR

This paper investigates Anderson localization transitions in 2D and 3D systems with quasiperiodic potentials, revealing that in 3D the transition universality class matches that of random potentials, while in 2D it differs.

Contribution

The study introduces higher-dimensional self-dual models generalizing the Aubry-André model and compares localization transition universality classes between random and quasiperiodic potentials.

Findings

In 3D, localization transition universality class matches that of random potentials.

In 2D, quasiperiodic potentials change the universality class of the transition.

Randomness is irrelevant at 3D Anderson localization transitions.

Abstract

We explore single-particle Anderson localization due to nonrandom quasiperiodic potentials in two and three dimensions. We introduce a class of self-dual models that generalize the one-dimensional Aubry-Andr\'e model to higher dimensions. In three dimensions (3D) we find that the Anderson localization transitions appear to be in the same universality class as for random potentials. In scaling or renormalization group terms, this means that randomness of the potential is irrelevant at the Anderson localization transitions in 3D. In two dimensions (2D) we also explore the Ando model, which is in the symplectic symmetry class and shows an Anderson localization transition for random potentials. Here, unlike in 3D, we find that the universality class changes when we instead use a quasiperiodic potential.