Altermagnets, a newly classified type of collinear magnet, exhibit zero magnetization, akin to antiferromagnets, but have spin-split electronic bands, akin to ferromagnets. Their low-energy excitations are predicted to be magnons, but with linear energy-momentum dispersion, typical of antiferromagnets, and additional chiral splitting analogous to those of electronic bands. However, such predictions are made using linear spin wave theory, which considers infinitely long-lived noninteracting magnons. This study employs nonperturbative quantum many-body calculations, via tensor network algorithms, to find how a chiral magnon will acquire finite lifetime and how the bands will shift due to magnon-magnon interaction. Such corrections to noninteracting magnon bands could be detected by Raman scattering experiments, for which the recipe is provided. Although the same interaction effects are often described in magnetism by nonlinearity of the Landau-Lifshitz-Gilbert equation, direct comparison using altermagnetic magnons as the testbed, shows how such classical methods cannot fully reproduce the results of quantum many-body calculations.
