  Magnon dynamics in skyrmion lattices have garnered significant interest due
to their potential applications in topological magnonics. Existing theories
often follow a single-momentum approach, assuming significant
Dzyaloshinskii-Moriya Interaction (DMI) to minimize the skyrmion's dimensions,
which can lead to oversimplification in describing magnon behavior. This study
introduces a multi-momentum operator theory for magnons in large 2D skyrmions,
where each skyrmion encompasses several thousand spins. The proposed theory
fully transforms the magnon Hamiltonian into momentum space, incorporating
off-diagonal terms to capture umklapp scattering caused by the skyrmion wave
vectors. Our results reveal deviations from single-momentum theories,
demonstrating that flat bands are not universal features of the skyrmionic
magnon spectrum. Additionally, we find that manipulating the skyrmion size with
an external magnetic field induces multiple topological phase transitions. At
high magnetic fields, the low-energy magnon spectrum becomes densely packed and
entirely topological, resembling a topological band continuum.
