Generic continuous spectrum for multi-dimensional quasi periodic Schr\"odinger operators with rough potentials

We study the multi-dimensional operator $(H_x u)n=\sum{|m-n|=1}u_{m}+f(T^n(x))u_n$,where$T$istheshiftofthetorus$\T^d$\mathrm{.}When$d=2$,weshowthespectrumof$H_x$ is almost surely purely continuous for a.e. $\alpha$ and generic continuous potentials. When $d\ge 3$, the same result holds for frequencies under an explicit arithmetic criterion. We also show that general multi-dimensional operators with measurable potentials do not have eigenvalue for generic $\alpha$.