Roton minimum as fingerprint of magnon-Higgs scattering in ordered quantum antiferromagnets

A quantitative description of magnons in long-range ordered quantum antiferromagnets is presented which is consistent from low to high energies. It is illustrated for the generic $S=1\mathrm{/}2$ Heisenberg model on the square lattice. The approach is based on a continuous similarity transformation in momentum space using the scaling dimension as truncation criterion. Evidence is found for significant magnon-magnon attraction inducing a Higgs resonance. The high-energy roton minimum in the magnon dispersion appears to be induced by strong magnon-Higgs scattering.