# Static Magnetic Response of Non-Fermi Liquid Density

## TL;DR

This paper demonstrates that the static magnetic response of fermion densities, including non-Fermi liquids, depends solely on the Fermi volume and Berry curvature, regardless of interactions, under broad theoretical assumptions.

## Contribution

It proves that the magnetic response of interacting fermions is determined by Fermi surface properties, extending known results from non-interacting systems to all orders in perturbation theory.

## Key findings

- Response depends on Fermi volume and Berry curvature
- Result holds for Fermi liquids and non-Fermi liquids
- Applicable to all orders in perturbation theory

## Abstract

We consider the response of the density of a fermion ensemble to an applied weak static magnetic field. It is known that for non-interacting 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 Fermi liquid and 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.