Orbital Magnetization within Self-Consistent Hartree-Fock via an Envelope Theorem
Abstract
Orbital magnetization is an elementary thermodynamic response function of a quantum system: the derivative of the grand potential with respect to magnetic field. However, naive perturbation theory is fraught with difficulties, as even infinitesimal magnetic fields shatter any bands into a Hofstadter butterfly spectrum. Even at the self-consistent Hartree-Fock (mean field) level, rigorous formulas for the orbital magnetization have only become available within the last year. This work provides a straightforward derivation of orbital magnetization at the mean field level using a completely real-space approach. The key tools used are the magnetic perturbation theory developed in the 1960s and an envelope theorem, which is a standard result in the calculus of variations. For simplicity, we restrict to insulating states at zero temperature on the infinite plane. We also discuss the natural connections to projected position operators and quantum geometry, as well as practical numerical computations.
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BibTeX
@misc{parker2026orbital,
title = {{Orbital Magnetization within Self-Consistent Hartree-Fock via an Envelope Theorem}},
author = {Daniel E Parker},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27624},
eprint = {2610.27624},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27624},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Orbital Magnetization within Self-Consistent Hartree-Fock via an Envelope Theorem
AU - Daniel E Parker
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27624
UR - https://arxiv.org/abs/2610.27624
AB - Orbital magnetization is an elementary thermodynamic response function of a quantum system: the derivative of the grand potential with respect to magnetic field. However, naive perturbation theory is fraught with difficulties, as even infinitesimal magnetic fields shatter any bands into a Hofstadter butterfly spectrum. Even at the self-consistent Hartree-Fock (mean field) level, rigorous formulas for the orbital magnetization have only become available within the last year. This work provides a straightforward derivation of orbital magnetization at the mean field level using a completely real-space approach. The key tools used are the magnetic perturbation theory developed in the 1960s and an envelope theorem, which is a standard result in the calculus of variations. For simplicity, we restrict to insulating states at zero temperature on the infinite plane. We also discuss the natural connections to projected position operators and quantum geometry, as well as practical numerical computations.
ER -