Universal scaling of quantum caustics in the dynamics of interacting particles

TL;DR

This paper investigates the universal scaling behavior of quantum caustics in the dynamics of the transverse-field Ising model, revealing a robust 2/3 exponent associated with Airy function catastrophes that persists across phases and perturbations.

Contribution

It demonstrates the universal 2/3 scaling exponent of quantum caustics in the transverse-field Ising model and shows its robustness against perturbations and boundary effects.

Findings

Universal 2/3 scaling exponent in quantum caustics

Scaling persists across the paramagnetic phase and near the quantum phase transition

Edge effects influence interference patterns but not the scaling exponent

Abstract

Recent theoretical studies have predicted the existence of caustics in many-body quantum dynamics, where they manifest as extended regions of enhanced probability density that obey temporal and spatial scaling relations. Focusing on the transverse-field Ising model, we investigate the dynamics initiated by a local quench in a spin chain, resulting in outward-propagating excitations that create a distinct caustic pattern. We calculate the scaling of the first two maxima of the interference fringes dressing the caustic, finding a universal exponent of 2/3, associated with an Airy function catastrophe. We demonstrate that this property is universal in the entire paramagnetic phase of the model, and starts varying at the quantum phase transition (QPT). This robust scaling persists even under perturbations that break the integrability of the model. We additionally explore the effect of boundary conditions and find that open boundaries introduce significant edge effects, leading to complex interference patterns. Despite these edge-induced dynamics, the overall power-law scaling exponent remains robust. These findings highlight the potential of quantum caustics as a powerful diagnostic tool for QPTs, demonstrating resilience against integrability-breaking perturbations and boundary condition variations.