# Non-Abelian gauge potential driven localization transition in quasiperiodic optical lattices

## TL;DR

This paper explores how non-Abelian gauge potentials influence localization transitions in quasiperiodic optical lattices, revealing a richer phase structure than in traditional Abelian models, with potential implications for understanding Anderson localization.

## Contribution

It introduces a non-Abelian generalization of the Aubry-Andre-Harper model and uncovers new localization phases driven by non-Abelian gauge effects.

## Key findings

- Non-Abelian AAH models exhibit self-duality under Fourier transformation.
- Localization transition includes coexistence phases not present in Abelian models.
- Non-Abelian gauge drives a transition from delocalization to localization through intermediate phases.

## Abstract

Gauge potential is an emergent concept in systems of ultracold atomic gases. Derived from quantum waves immersed in an \emph{Abelian} gauge, the quasiperiodic Aubry-Andre-Harper (AAH) model is a simple yet powerful Hamiltonian to study the Anderson localization of ultracold atoms. In this work, we investigate the localization properties of ultracold atoms trapped in quasiperiodic optical lattices subject to a non-Abelian gauge, which can be depicted by a family of non-Abelian AAH models. We identify that the non-Abelian AAH models can bear the self-duality under the Fourier transformation. We thus analyze the localization transition of this self-dual non-Abelian quasiperiodic optical lattices, revealing that the non-Abelian gauge involved drives a transition from a pure delocalization phase, then to coexistence phases, and then finally to a pure localization phase. This is in stark contrast to the Abelian AAH model that does not support the coexistence phases. Our results thus comprise a new insight on the fundamental aspects of Anderson localization in quasiperiodic systems, from the perspective of non-Abelian gauge.