Robustness of a Local Fermi Liquid against Ferromagnetism and Phase Separation

We study the properties of Fermi liquids with the microscopic constraint of a local self-energy. In this case the forward scattering sum rule imposes strong limitations on the Fermi-liquid parameters, which rule out any Pomeranchek instabilities—both ferromagnetism and phase separation are suppressed. Superconductivity is possible in an $s$-wave channel only. We also study the approach to the metal-insulator transition, and find a Wilson ratio approaching 2. This ratio and other properties of ${\mathrm{Sr}}_{1-x}{\mathrm{La}}_x{\mathrm{TiO}}_3$ are all consistent with the local Fermi-liquid scenario.