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 over 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. These findings highlight the potential of quantum caustics to act as powerful diagnostic tools for QPTs in the dynamics of interacting many-body quantum systems.

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• Collective effects in quantum optics
• Dynamical phase transitions
• Magnetic coupling
• Quantum chaos
• Quantum correlations in quantum information
• Quantum phase transitions
• Quantum quench
• Spin dynamics
• Chaos & nonlinear dynamics
• Integrable systems
• Ising model
• Many-body techniques
• Quantum spin chains
• Scaling methods
• Tensor network methods