On optimal Wannier decay in dimension three
Simon Becker, Zhongkai Tao, Mengxuan Yang
Abstract
For a Chern nontrivial Bloch bundle over the three torus, we construct an orthonormal Wannier basis with the optimal pointwise decay O(|x|-5/2). All but one of the generators decay exponentially. This resolves the question left open in arXiv:2505.01999.
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