Non-peturbative density expansions for extended Coulomb systems

Abstract

We present a general non-perturbative argument that combines the Pauli and virial theorems for a multicomponent translationally invariant Coulombic system of fermions at zero temperature, and which by an iteration procedure leads to a series in rs representing the total energy per particle. It agrees with the form found for the ground state of an electron gas in a uniform positive background by diagrammatic perturbation theory, but is shown to be valid for more general (translationally invariant) multicomponent Coulombic systems as well. Several modifications of the method are also discussed, one of them being applied to a low-density single-component system with inhomogeneous states

it yields the expected result for a harmonic Wigner crystal and a rigorous proof that this state (or any other state with harmonic excitations) must be an insulator.