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arXiv · 1904.13051

Good Wannier bases in Hilbert modules associated to topological insulators

Matthias Ludewig·Guo Chuan Thiang
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Abstract

For a large class of physically relevant operators on a manifold with discrete group action, we prove general results on the (non-)existence of a basis of smooth well-localised Wannier functions for their spectral subspaces. This turns out to be equivalent to the freeness of a certain Hilbert module over the group $C^*$-algebra canonically associated to the spectral subspace. This brings into play $K$-theoretic methods and justifies their importance as invariants of topological insulators in physics.

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BibTeXRIS

Matthias Ludewig, Guo Chuan Thiang. 2020-06-21. Good Wannier bases in Hilbert modules associated to topological insulators. https://doi.org/10.1063/1.5143493

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