Projectification of point group symmetries with a background flux and the Lieb-Schultz-Mattis theorem
Abstract
We discuss the Lieb-Schultz-Mattis (LSM) theorem in two-dimensional spin systems with on-site ${\mathrm U}(1)\rtimes {\mathbb Z}_2$ spin rotation symmetry and point group $C_{2v}$ symmetry about a site. We ``twist" the point group symmetry by introducing a small uniform U(1) flux to obtain a projective symmetry, similarly to the familiar magnetic translation symmetry. The LSM theorem is proved in presence of the flux and then it is demonstrated that the theorem holds also for the flux-free system. Besides, the uniform flux enables us to show the LSM theorem for the time-reversal symmetry and the site-centered $C_2$-rotation symmetry.
Fields of Study & Subjects
Methane Hydrates and Related Phenomena
Scientific Research and Discoveries
Publication details
- Journal / source
- Physical review. B./Physical review. B
- Publisher
- American Physical Society (APS)
- Volume
- 113
- Issue
- 9
- Publication date
- 23 February 2026
- Language
- EN