Luttinger theorem for a spin-density-wave state

TL;DR

This paper derives an analog of the Luttinger relation for a spin-density-wave state, revealing modifications in the occupied states' area and highlighting anomalies that prevent a straightforward perturbative proof.

Contribution

It introduces a modified Luttinger relation for spin-density-wave states and discusses the limitations of perturbative approaches due to anomalies.

Findings

Modified relation between occupied state area and particle density

Presence of an anomaly similar to the chiral anomaly

Perturbative methods are insufficient for the Luttinger theorem in this context

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.