  Using projected entangled-pair states (PEPS) we analyze the localization
properties of two-dimensional systems on a square lattice. We compare the
dynamics found for three different disorder types: (i) quenched disorder, (ii)
sum of two quasi-periodic potentials along both spatial dimensions and (iii) a
single quasi-periodic potential rotated with respect to the underlying lattice
by a given angle. We establish the rate of loss of information, a quantity
measuring the error made while simulating the dynamics, as a good hallmark of
localization physics by comparing to entanglement build-up as well as the
inverse participation ratio in exactly solvable limits. We find that the
disorder strength needed to localize the system increases both with the
dimensionality of as well as the interaction strength in the system. The first
two cases of potential (i) and (ii) behave similar, while case (iii) requires
larger disorder strength to localize.
