Phys. Rev. Lett. 86, 5341–5344 (2001)Exponential Decay Properties of Wannier Functions and Related QuantitiesReceived 19 January 2001; published in the issue dated 4 June 2001 The spatial decay properties of Wannier functions and related quantities have been investigated using analytical and numerical methods. We find that the form of the decay is a power law times an exponential, with a particular power-law exponent that is universal for each kind of quantity. In one dimension we find an exponent of -3/4 for Wannier functions, -1/2 for the density matrix and for energy matrix elements, and -1/2 or -3/2 for different constructions of nonorthonormal Wannier-like functions. © 2001 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.86.5341
DOI:
10.1103/PhysRevLett.86.5341
PACS:
71.15.Ap, 71.20.-b
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