Non-perturbative localization for quasi-periodic Jacobi block matrices

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.