Generalized many-body exciton g-factors: magnetic hybridization and non-monotonic Rydberg series in monolayer WSe2

The magneto-optical response of excitons in monolayer transition-metal dichalcogenides is governed by a complex interplay of Bloch-state quantum geometry—reflected in the electronic magnetic moment -- coupled with interband mixing and many-body interactions. Here, we develop a robust and general first-principles framework for many-body exciton g-factors (magnetic moments) by incorporating off-diagonal terms for the spin and orbital angular momenta of single-particle bands and many-body states under magnetic fields pointing in arbitrary spatial directions. We implement our framework using many-body perturbation theory via the GW-Bethe-Salpeter equation (BSE) and supplement our analysis with symmetry-based models. Focusing on the archetypal monolayer WSe2, we accurately reproduce the known results of the low-energy excitons, including Zeeman splitting and dark/gray exciton brightening. Furthermore, our theory naturally reveals the magnetic-field hybridization of higher-energy excitons (s-, p-, and d-like) and shows that the magnetic moments of nodal excitons (p- and d-like) do not acquire additional ±m_j*μ_B contributions (m_j = 1, 2), characteristic of the hydrogenic picture. Importantly, our approach resolves the long-standing puzzle of the experimentally measured non-monotonic Rydberg series (1s-4s) of exciton g-factors. Our framework offers a comprehensive route to investigate, rationalize, and predict the nontrivial interplay between magnetic fields, angular momenta, and many-body exciton physics in van der Waals systems, opening new opportunities to probe signatures of quantum geometry within many-body states. [arXiv:2505.18468]