an:07277874
Zbl 1452.82024
Ludewig, Matthias; Thiang, Guo Chuan
Good Wannier bases in Hilbert modules associated to topological insulators
EN
J. Math. Phys. 61, No. 6, 061902, 22 p. (2020).
00455589
2020
j
82D20 82D40 35Q55 82C20
Wannier bases; topological insulators
Summary: 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 well-localized 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 with the spectral subspace. This brings into play \(K\)-theoretic methods and justifies their importance as invariants of topological insulators in physics.
{\copyright 2020 American Institute of Physics}