Phys. Rev. Lett. 82, 2127–2130 (1999)Locality of the Density Matrix in Metals, Semiconductors, and InsulatorsReceived 15 April 1998; published in the issue dated 8 March 1999 We present an analytical study of the spatial decay rate γ of the one-particle density matrix ρ(r⃗,r⃗′)∼exp(-γ|r⃗-r⃗′|) for systems described by single-particle orbitals in periodic potentials in arbitrary dimensions. This decay reflects electronic locality in condensed matter systems and is also crucial for O(N) density functional methods. We find that γ behaves contrary to the conventional wisdom that generically γ∝√Δ in insulators and γ∝√T in metals, where Δ is the direct band gap and T is the temperature. Rather, in semiconductors γ∝Δ, and in metals at low temperature γ∝T. © 1999 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.82.2127
DOI:
10.1103/PhysRevLett.82.2127
PACS:
71.15.Mb, 71.20.-b, 71.23.An
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