Non-perturbative localization for quasi-periodic Jacobi block matrices

TL;DR

This paper establishes non-perturbative Anderson localization for quasi-periodic Jacobi block matrices with Diophantine rotation dynamics, extending results to various physical models.

Contribution

It provides the first non-perturbative proof of localization for these operators under general conditions, including applications to multiple physical systems.

Findings

Proves localization assuming non-zero Lyapunov exponents.

Derives arithmetic localization results for one-dimensional cases.

Discusses applications to models like stacked graphene and XY spin chains.

Abstract

We prove non-perturbative Anderson localization for quasi-periodic Jacobi block matrix operators assuming non-vanishing of all Lyapunov exponents. The base dynamics on tori $\mathbb{T}^b$ is assumed to be a Diophantine rotation. Results on arithmetic localization are obtained for $b=1$, and applications to the skew shift, stacked graphene, XY spin chains, and coupled Harper models are discussed.