Combining magnetometry with optical spectroscopy has uncovered novel quantum phenomena and is emerging as a powerful probe of quantum materials. However, the theory of the magnetic response of excitons, correlated electron-hole pairs in insulators, remains incomplete due to insufficient treatment of electron-hole interactions and quantum geometric effects. In biased bilayer graphene, for instance, theoretical predictions of valley $g$ factors for $p$ excitons deviate from experiment by nearly an order of magnitude. Here, we develop a quantum theory of the exciton orbital magnetic moment, based on first-order perturbation theory within the GW plus Bethe-Salpeter equation approach and a rigorous treatment of the position operator in the response of exciton states to a magnetic field. Our formalism reveals three distinct contributions that go beyond the heuristic approaches used in the literature: a Berry-phase-corrected single-particle electron and hole moment difference, a term from envelope-function winding linked to electron-hole relative motion, and a center-of-mass correction from exciton band quantum geometry, with the latter two being completely new effects not considered in previous studies. Our ab initio calculations yield results in excellent agreement with experiment, establishing the importance of interaction and quantum geometric effects in the magnetic response of excitons.

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• Berry curvature
• Bethe-Salpeter equation
• Excitons
• First-principles calculations
• GW method