Proof of geometric Borg's Theorem in arbitrary dimensions

Wencai Liu

Let $\hat{I}”+V$ be the discrete Schrödinger operator, where $\hat{I}”$ is the discrete Laplacian on ${\mathbb{Z}}^d$ and potential $V:{\mathbb{Z}}^d\to \mathbb{C}$ is $\hat{I}“$-periodic with $Γ=q_1\…