Orbital Magnetization of Interacting Electrons

TL;DR

This paper derives an exact formula for the orbital magnetization of interacting electrons, applicable across interaction strengths and temperatures, extending beyond mean-field approximations and enabling studies of strongly correlated systems.

Contribution

It provides a novel, exact expression for orbital magnetization in interacting electron systems, generalizing previous theories and applicable to both weakly and strongly correlated regimes.

Findings

The formula matches known results for non-interacting and weakly interacting electrons.

It extends the modern theory of orbital magnetization to include interactions.

The framework is suitable for studying strongly correlated electrons in magnetic fields.

Abstract

We derive an exact expression for the orbital magnetization of electrons with short-range interactions (such as density-density interactions) in terms of exact zero-frequency response functions of the zero-field system. The result applies to weakly and strongly correlated electrons at zero and finite temperature, provided that the local grand potential density only depends on local thermodynamic parameters. We benchmark the formula for non-interacting and weakly-coupled electrons. To zeroth and first orders in the interaction strength, it agrees with the modern theory of orbital magnetization and its recent generalization to self-consistent Hartree-Fock bands. Our work provides an exact framework of interacting orbital magnetization beyond mean-field treatments, and paves the way for quantitative studies of strongly correlated electrons in external magnetic fields.