  The energy-momentum dispersion of magnons, viewed as noninteracting and
infinitely long-lived quasiparticles describing collective low-energy
excitations of magnetic materials, is often presented as sharp bands obtained
from the effective quantum spin Hamiltonian, after being simplified via
linearized Holstein-Primakoff (HP) transformations. However, magnons are prone
to many-body interactions with other quasiparticles which can lead to their
spontaneous decay. The magnon-magnon interactions could affect newly classified
altermagnets. On the other hand, sharp bands of noninteracting chiral magnons
in RuO2, as the canonical example of altermagnets, have been very recently
predicted. Here, we employ nonperturbative numerically (quasi)exact quantum
many-body calculations, via time-dependent matrix product states (TDMPS), to
obtain magnon spectral function of RuO2. These calculations produce a broadened
magnon dispersion, which overlaps with linearized HP theory sharp bands only at
edges/center of the Brillouin zone. Substantially deviating otherwise.
Artificially making exchange interaction within two sublattices of RuO2 closer
in value forces these two spectra to overlap, thereby explaining the origin of
the failure of linearized HP theory. Such features translate into the
difference between their respective density of states, which we also compute
and which could be tested by Raman scattering experiments. Finally, we employ
popular Landau-Lifshitz-Gilbert (LLG) equation-based classical atomistic spin
dynamics (ASD) simulations to obtain dynamical structure factor and extract
magnon spectrum from it at finite temperature. Despite including magnon-magnon
interactions via nonlinearity of LLG equation, ASD simulations cannot fully
match the TDMPS-computed magnon spectrum due to nonclassical effects harbored
by altermagnets.
