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Polarization fluctuations in insulators and metals: New and old theories merge

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arxiv cond-mat/0512247 v2 pith:MMTUA5OM submitted 2005-12-12 cond-mat.mtrl-sci cond-mat.other

R. Resta This is my paper · ORCID
classification cond-mat.mtrl-scicond-mat.other
keywords metalsrulefinitefluctuationfluctuationsgeneralizedinsulatorspolarization
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The ground-state fluctuation of polarization P is finite in insulators and divergent in metals, owing to the SWM sum rule [I. Souza, T. Wilkens, and R. M. Martin, Phys. Rev. B 62, 1666 (2000)]. This is a virtue of periodic (i.e. transverse) BCs. I show that within any other boundary conditions the P fluctuation is finite even in metals, and a generalized sum rule applies. The boundary-condition dependence is a pure correlation effect, not present at the independent-particle level. In the longitudinal case div P = -rho, and one equivalently addresses charge fluctuations: the generalized sum rule reduces then to a well known result of many-body theory.

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