Work

Wannier Decay and the Thouless Conjecture

Year: 2026

Type: article

Abstract: Nontrivial Chern classes pose an obstruction to the existence of exponentially decaying Wannier functions that provide natural bases for spectral subspaces. For nontrivial Bloch bundles, we obtain decay rates of Wannier functions in dimensions $d=2,3$. For $d=2$, we construct Wannier functions with full asymptotics and optimal decay rate $\mathcal{O}(|x|^{-2})$ as conjectured by Thouless; for $d=3$, we construct Wannier functions with the uniform decay rate $\mathcal{O}(|x|^{-7/3})$.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnag093

Authors: Simon Becker, Zhongkai Tao, Mengxuan Yang

Institutions: ETH Zurich, Institute for Mathematical Research, Institut des Hautes Études Scientifiques, Princeton University

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,534

Funder: Statens Naturvidenskabelige Forskningsrad