Fig. 4: Alternative understanding of Van Hove singularities as caustic features in the collective spin dynamics.
From: Van Hove singularity in the magnon spectrum of the antiferromagnetic quantum honeycomb lattice
a Caustic features in ray optics. Parallel light rays (black lines) enter an optical system at different positions. When these light rays reflecting from a circular mirror (red line) coalesce, they give rise to caustic features in real space. b Caustic features in a spin response. The two-magnon continuum can be understood as a sum of sharp contributions, ω = εk + εq−k, each corresponding to a fixed momentum k of the first magnon. When these sharp contributions (black lines) coalesce, they give rise to caustic features in the two-magnon continuum. Note that the spin response shown here is for a one-dimensional model system; for the two-dimensional system in consideration, the caustic features appear inside the continuum (not at its edge) and are weaker as they correspond to logarithmic (rather than square-root) singularities.
