Ward identities and orbital magnetization in current density functional theory

TL;DR

This paper derives a new formula for orbital magnetization in periodic crystals within current density functional theory, linking it to the Kohn-Sham eigenfunctions and a Ward identity.

Contribution

It provides a novel derivation of the orbital magnetization formula using linear response and reveals a Ward identity connecting current vertex and self-energy derivatives.

Findings

Confirmed the orbital magnetization can be computed exactly from Kohn-Sham eigenfunctions.

Derived a Ward identity linking current vertex to self-energy derivative.

Presented a new linear response derivation in the long-wavelength limit.

Abstract

We revisit the derivation of the orbital magnetization formula for periodic crystals in current density functional theory (CDFT)[1]. Our new derivation computes the linear response of the energy density to a periodic magnetic field in the long-wavelength limit. We unveil a Ward identity which connects the current vertex to the derivative of the Kohn-Sham self-energy. The result of Ref.[1] is confirmed: the orbital magnetization of the interacting solid can be computed exactly (in principle) from the self-consistent eigenfunctions and eigenvalues of the Kohn-Sham equation of CDFT.