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

Static Magnetic Response of Non-Fermi Liquid Density