Consider the Anderson model given by the Hamiltonian $H \in B(l^2( \mathbb{Z}^d)) $ defined by $H = - \Delta + V$ where the potential $V$ acts on a unit vector $ \vert x \rangle \in l^2( \mathbb{Z}^d)$ by $V \vert x \rangle = V(x) \vert x \rangle $ where $V(x)$ are i.i.d uniformly distributed in $\lbrack 0,1 \rbrack$. This system exhibits Anderson localization.
Now, if we put $d=1$ and I pick $V(2x) $ i.i.d uniformly distributed in $\lbrack 0,1 \rbrack$ and then let $V(2x+1) = V(2x)$. Does this system then still exhibit Anderson localization?
