Scattering theory of chiral edge modes in topological magnon insulators

Topological magnon insulators exhibit robust edge modes with chiral properties similar to quantum Hall edge states. However, due to their strong localization at the edges, interactions between these chiral edge magnons can be significant, as we show in a model of coupled magnon-conserving spin chains in an electric field gradient. The chiral edge modes remain edge-localized and do not scatter into the bulk, and we characterize their scattering phase: for strongly localized edge modes, we observe significant deviation from the bare scattering phase. This renormalization of edge scattering can be attributed to bound bulk modes resonating with the chiral edge magnons in the spirit of Feshbach resonances in atomic physics. We argue that the scattering dynamics can be probed experimentally with a real-time measurement protocol using inelastic scanning tunneling spectroscopy. Our results show that interaction among magnons can be encoded in an effective edge model of reduced dimensionality, where the interactions with the bulk renormalize the effective couplings. Our work introduces a systematic way to determine the many-body effective theory for edge states in topological magnon insulators.