On optimal Wannier decay in dimension three

Abstract

For a Chern nontrivial Bloch bundle over the three torus, we construct an orthonormal Wannier basis with the optimal pointwise decay $\mathcal{O}(|x{|}^{-5/2})$. All but one of the generators decay exponentially. This resolves the question left open in arXiv:2505.01999.

arXiv comment8 pages, comments are welcome