Hana Rebecca Schiff
The aim of this tutorial is to provide a pedagogical introduction to the theory of spin groups and their representation theory. We will present a classification of the spin groups, initiated by Litvin & Opechowski [1,2], and extensively studied in recent years [3-6]. Then, we will shift our attention to (co-)representation theory, especially focusing on the crystallographic spin point groups [7]. Here, we will explore the extent to which spin groups provide information beyond the magnetic groups, and differentiate between scenarios in which spin group theory is and is not necessary. We will conclude by commenting on applications of spin group theory.
[1] D. Litvin and W. Opechowski, Physica 76 (3), 538 (1974)[2] D. B. Litvin, Acta Crystallographica Section A 33 (2), 279 (1977)
[3] N. Lazic et al., Acta Crystallographica Section A 69 (6), 611 (2013)
[4] P. Liu et al., Phys. Rev. X 12, 021016 (2022)
[5] Z. Xiao et al., Phys. Rev. X 14, 031037 (2024)
[6] X. Chen et al., Phys. Rev. X 14, 031038 (2024)
[7] H. Schiff et al., SciPost Phys. 18, 109 (2025)