The Coulomb force and the various thermodynamic phases of simple metals

With just two-body Coulomb interactions between electrons being taken into account, the phase diagram of a simple metal includes the following phases at least: the ordinary paramagnetic Fermi liquid, itinerast ferromagnetism, a charge-density wave phase and an antiferromagnetic phase (either of which can be insulating), and surprisingly a superconducting phase. This paper surveys the physics of the Coulomb interactions in metals, and the diverse roles played by the zero-range Hubbard interaction U0 and the long-range Coulomb interactions denoted ΔV(q). Screening of the latter by the currents in the metal is treated in some detail. This paper is intended as an introduction into an important area of solid-state physics. A number of novel ideas are proposed, but are clearly identified as such. For example: although V(q) = U0 + δV(q) is required to be positive at all q, v(q) = (1/2)U0 + ΔV(q) is not. The authors show that if v(q) < 0 in a given phase, that phase is unstable (regardless of band structure, etc.) The authors also find that the Coulomb repulsion between electrons in a given band is somewhat stronger than that between holes