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On the construction of composite Wannier functions. (English) Zbl 1357.82069
The existence and construction of exponentially localized Wannier functions is one of the fundamental problems in solid-state physics. The authors give a constructive proof for the existence of a Bloch basis of rank $$N$$ which is both smooth and periodic with respect to its $$d$$-dimensional quasi-momenta, when $$1\leq d\leq 2$$ and $$N\geq 1$$. Also it is shown that, by adding a weak, globally bounded but not necessarily constant magnetic field, the existence of a localized basis is preserved.

##### MSC:
 82D20 Statistical mechanical studies of solids 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
##### Keywords:
composite Wannier functions; Bloch basis; localization
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##### References:
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