Orbital Magnetization from Uniform and Periodic Magnetic Fields
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910260553318400 |
|---|---|
| author | Huang, Chunli |
| author_facet | Huang, Chunli |
| contents | Magnetization is thermodynamically defined as the derivative of the grand potential with respect to a uniform magnetic field. However, a uniform magnetic field makes the kinetic momentum operators noncommuting and Landau-quantizes the electron motion. This changes the zero-field momentum-space to Landau-levels and raises a fundamental question: how can the thermodynamic response to a uniform field be reproduced by a linear-response calculation carried out in the momentum space of the zero-field problem? We address this question analytically in a quantum Hall ferromagnet that allows the orbital magnetization $M$ to be computed in a closed form. We first compute $M$ from the local Hartree--Fock projector response to a periodic magnetic field with zero net flux. We then compute $M$ from the derivative of the grand potential with respect to a uniform magnetic field along the Středa line. The two approaches give the same result, even though the first keeps the Hilbert space fixed while the second changes the Landau-level degeneracy. Their agreement suggests that we should view orbital magnetization as the energy associated with the spectral flow that gives rise to the Středa formula. Our work provides a tutorial introduction to orbital magnetization and its relation to the Středa formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26889 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Orbital Magnetization from Uniform and Periodic Magnetic Fields Huang, Chunli Mesoscale and Nanoscale Physics Materials Science Magnetization is thermodynamically defined as the derivative of the grand potential with respect to a uniform magnetic field. However, a uniform magnetic field makes the kinetic momentum operators noncommuting and Landau-quantizes the electron motion. This changes the zero-field momentum-space to Landau-levels and raises a fundamental question: how can the thermodynamic response to a uniform field be reproduced by a linear-response calculation carried out in the momentum space of the zero-field problem? We address this question analytically in a quantum Hall ferromagnet that allows the orbital magnetization $M$ to be computed in a closed form. We first compute $M$ from the local Hartree--Fock projector response to a periodic magnetic field with zero net flux. We then compute $M$ from the derivative of the grand potential with respect to a uniform magnetic field along the Středa line. The two approaches give the same result, even though the first keeps the Hilbert space fixed while the second changes the Landau-level degeneracy. Their agreement suggests that we should view orbital magnetization as the energy associated with the spectral flow that gives rise to the Středa formula. Our work provides a tutorial introduction to orbital magnetization and its relation to the Středa formula. |
| title | Orbital Magnetization from Uniform and Periodic Magnetic Fields |
| topic | Mesoscale and Nanoscale Physics Materials Science |
| url | https://arxiv.org/abs/2605.26889 |