Static Magnetic Response of Non-Fermi-Liquid Density

We consider the response of the density of a fermion ensemble to an applied weak static magnetic field. It is known that, for a noninteracting Fermi gas, this response is fully characterized by the Fermi volume and the Berry curvature on the Fermi surface. Here we show the same result holds for interacting fermions, including a Fermi liquid and a non-Fermi liquid, to all orders in perturbation theory. Our result relies only on the assumption of a well-defined Fermi surface and the general analytic properties of quantum field theory, and is completely model independent.