Anderson localization for the unitary almost Mathieu operator

Abstract We prove Anderson localization for all Diophantine frequencies and all non-resonant phases for a model that arises from a 2D quantum walk model subject to an external magnetic field, also known as the unitary almost Mathieu operator. Our work provides the first localization results for all Diophantine frequencies in quasi-periodic quantum walk and CMV matrix setting. We also obtain sharp asymptotics of the localized eigenfunctions.