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We study quasiparticle dynamics in two-dimensional (2D) integrable Kitaevhoneycomb model both without and in the presence of an external periodic drive.We identify light-cones in wavefunction propagation as a signature of quantumcaustic, i.e. bright structures formed during quantum dynamics analogous tothat of imperfect focusing in geometrical optics. We show that this dynamicsfollows an angle in spatial direction and it is anisotropic with respect tomodel parameters. Using coalescence of critical points, we provide an exactsolution to the envelope of caustic, which corresponds to the Lieb-Robinsonbound in 2D. Further, consedering the system to be periodically driven, wepoint out that the caustic structure completely changes in presence of externaltime dependent drive.

Emergence of caustics in dynamics of the Kitaev model