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

TL;DR

This paper demonstrates that polarization fluctuations depend on boundary conditions, with finite fluctuations in metals under non-periodic boundaries, revealing a boundary-condition-dependent correlation effect beyond independent-particle theories.

Contribution

It introduces a generalized sum rule for polarization fluctuations applicable under arbitrary boundary conditions, extending previous theories limited to periodic boundaries.

Findings

Polarization fluctuation is finite in metals with non-periodic boundary conditions.

Boundary conditions influence polarization fluctuation due to correlation effects.

A generalized sum rule relates polarization and charge fluctuations in various boundary scenarios.

Abstract

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.