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Good Wannier bases in Hilbert modules associated to topological insulators. (English) Zbl 1452.82024
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.
©2020 American Institute of Physics
MSC:
82D20 Statistical mechanical studies of solids
82D40 Statistical mechanical studies of magnetic materials
35Q55 NLS equations (nonlinear Schrödinger equations)
82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
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