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

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.

Changed title (old version was: Light-cones and quantum caustics in quenched spin chains), added new figures and extended the paper to include XY model. 20 pages, 10 figures

References in corpus (19)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Single-Spin Addressing in an Atomic Mott Insulator
• Quantum Quench in the Transverse Field Ising Chain
• Quantum Walk in Position Space with Single Optically Trapped Atoms
• Strongly Correlated Quantum Walks in Optical Lattices
• Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model
• Full counting statistics in a propagating quantum front and random matrix spectra
• Out-of-time-ordered correlators in quantum Ising chain
• Time evolution of correlations in strongly interacting fermions after a quantum quench
• Dynamics of a quantum phase transition in the 1D Bose-Hubbard model: excitations and correlations induced by a quench
• Out of Time Ordered Correlators and Entanglement Growth in the Random Field XX Spin Chain
• Hydrodynamical phase transition for domain-wall melting in the XY chain
• Light-cone velocities after a global quench in a non-interacting model
• Double light-cone dynamics establish thermal states in integrable 1D Bose gases
• Catastrophes in non-equilibrium many-particle wave functions: universality and critical scaling
• Caustic formation in expanding condensates of cold atoms

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• Effects of topological and non-topological edge states on information propagation and scrambling in a Floquet spin chain
• Domain wall dynamics in classical spin chains: free propagation, subdiffusive spreading, and soliton emission
• Caustics in the sine-Gordon model from quenches in coupled 1D Bose gases
• Dynamical Phase Transitions, Caustics, and Quantum Dark Bands
• Mechanisms of scrambling and unscrambling of quantum information in the ground state in spin chains: domain-walls, spin-flips and scattering phase shifts
• Ballistic propagation of a local impact in the one-dimensional $XY$ model
• Emergence of caustics in dynamics of the Kitaev model