Quantum caustics and the hierarchy of light cones in quenched spin chains

TL;DR

This paper demonstrates that light cone structures in quenched spin chains are quantum caustics described by catastrophe theory, revealing a hierarchy of structures, scaling laws, vortex networks, and sensitivity to phase transitions.

Contribution

It introduces a novel application of catastrophe theory to quantum field singularities, detailing the hierarchy of light cones and vortex dynamics in spin chains.

Findings

Light cone structures are quantum caustics modeled by catastrophe theory.

Explicit calculations for the Ising and XY models show specific catastrophes like fold and cusp.

Vortex pairs inside the cone are sensitive to phase transitions and critical exponents.

Abstract

We show that the light cone-like structures that form in spin chains after a quench are quantum caustics. Their natural description is in terms of catastrophe theory and this implies: 1) a hierarchy of light cone structures corresponding to the different catastrophes; 2) dressing by characteristic wave functions that obey scaling laws determined by the Arnol'd and Berry indices; 3) a network of vortex-antivortex pairs in space-time inside the cone. We illustrate the theory by giving explicit calculations for the transverse field Ising model and the XY model, finding fold catastrophes dressed by Airy functions and cusp catastrophes dressed by Pearcey functions; multisite correlation functions are described by higher catastrophes such as the hyperbolic umbilic. Furthermore, we find that the vortex pairs created inside the cone are sensitive to phase transitions in these spin models with their rate of production being determined by the dynamical critical exponent. More broadly, this work illustrates how catastrophe theory can be applied to singularities in quantum fields.