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The spatial decay properties of Wannier functions and related quantities havebeen investigated using analytical and numerical methods. We find that the formof the decay is a power law times an exponential, with a particular power-lawexponent that is universal for each kind of quantity. In one dimension we findan exponent of -3/4 for Wannier functions, -1/2 for the density matrix and forenergy matrix elements, and -1/2 or -3/2 for different constructions ofnon-orthonormal Wannier-like functions.

Exponential Decay Properties of Wannier Functions and Related Quantities