Luttinger theorem for a spin-density-wave state

Abstract

We obtained the analog of the Luttinger relation for a commensurate spin-density-wave state. We show that while the relation between the area of the occupied states and the density of particles gets modified in a simple and predictable way when the system becomes ordered, a perturbative consideration of the Luttinger theorem does not work due to the presence of an anomaly similar to the chiral anomaly in quantum electrodynamics.