Emergence of caustics in dynamics of the Kitaev model

TL;DR

This paper investigates quantum caustics in the quasiparticle dynamics of the 2D Kitaev honeycomb model, revealing anisotropic light-cones and how periodic driving alters caustic structures, with implications for Lieb-Robinson bounds.

Contribution

It provides an exact solution for the caustic envelope in the 2D Kitaev model and analyzes how external periodic drives modify quantum light-cone structures.

Findings

Identification of anisotropic light-cones as quantum caustics

Exact solution for the caustic envelope related to Lieb-Robinson bounds

Caustic structures are significantly altered by periodic driving

Abstract

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