Quantum caustics and the hierarchy of light cones in quenched spin chains
arXiv:1710.01289 · doi:10.1103/PhysRevResearch.1.033135
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 (61)
- Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
- Cold bosonic atoms in optical lattices
- A quantum gas microscope - detecting single atoms in a Hubbard regime optical lattice
- Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
- Evolution of Entanglement Entropy in One-Dimensional Systems
- Quantum many-body systems out of equilibrium
- Time-dependence of correlation functions following a quantum quench
- Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
- Transition from a strongly interacting 1D superfluid to a Mott insulator
- Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
- Observation of entanglement propagation in a quantum many-body system
- Light-cone-like spreading of correlations in a quantum many-body system
- Unifying time evolution and optimization with matrix product states
- Non-equilibrium coherence dynamics in one-dimensional Bose gases
- Non-local propagation of correlations in long-range interacting quantum systems
- 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
- Quantum simulation of frustrated magnetism in triangular optical lattices
- Microscopic observation of magnon bound states and their dynamics
- Strongly Correlated Quantum Walks in Optical Lattices
- Local emergence of thermal correlations in an isolated quantum many-body system
- Onset of a Quantum Phase Transition with a Trapped Ion Quantum Simulator
- Quantum Quench in the Transverse Field Ising chain I: Time evolution of order parameter correlators
- Spread of correlations in long-range interacting quantum systems
- Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model
- Entanglement growth in quench dynamics with variable range interactions
- Sub-Poissonian fluctuations in a 1D Bose gas: from the quantum quasi-condensate to the strongly interacting regime
- Full counting statistics in a propagating quantum front and random matrix spectra
- Out-of-time-ordered correlators in quantum Ising chain
- Breakdown of quasilocality in long-range quantum lattice models
- Bogoliubov-Cerenkov radiation in a Bose-Einstein condensate flowing against an obstacle
- Inhomogeneous field theory inside the arctic circle
- Quantum catastrophe of slow light
- Time evolution of correlations in strongly interacting fermions after a quantum quench
- Between a metal and an insulator: the critical state of the Anderson transition
- Observation of scaling in the dynamics of a strongly quenched quantum gas
- Inhomogeneous quenches in a fermionic chain: exact results
- Propagation front of correlations in an interacting Bose gas
- Effect of disorder on quantum phase transitions in anisotropic XY spin chains in a transverse field
- Dynamic scaling of fronts in the quantum XX chain
- Inhomogeneous quenches in the transverse field Ising chain: scaling and front dynamics
- Universal Scaling Laws for Correlation Spreading in Quantum Systems with Short- and Long-Range Interactions
- Ballistic front dynamics after joining two semi-infinite quantum Ising chains
- Universality and robustness of revivals in the transverse field XY model
- Dynamics of a quantum phase transition in the 1D Bose-Hubbard model: excitations and correlations induced by a quench
- Casimir forces and quantum friction from Ginzburg radiation in atomic BECs
- Out of Time Ordered Correlators and Entanglement Growth in the Random Field XX Spin Chain
- Caustic Skeleton & Cosmic Web
- Hydrodynamical phase transition for domain-wall melting in the XY chain
- Quantum and Classical Dynamics of a BEC in a Large-Period Optical Lattice
- Light-cone velocities after a global quench in a non-interacting model
- Universal equilibrium scaling functions at short times after a quench
- Quantum catastrophes and ergodicity in the dynamics of bosonic Josephson junctions
- Demonstration of fold and cusp catastrophes in an atomic cloud reflected from an optical barrier in the presence of gravity
- Double light-cone dynamics establish thermal states in integrable 1D Bose gases
- Observation of Caustics in the Trajectories of Cold Atoms in a Linear Magnetic Potential
- Quantum spin dynamics in Fock space following quenches: Caustics and vortices
- Catastrophes in non-equilibrium many-particle wave functions: universality and critical scaling
- Caustic formation in expanding condensates of cold atoms
- Diffraction catastrophes threaded by quantized vortex skeletons caused by atom-optical aberrations induced in trapped Bose-Einstein condensates
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- Universal dynamics of rogue waves in a quenched spinor Bose condensate
- Self-accelerating beam dynamics in the space fractional Schrödinger equation
- Scaling at the OTOC Wavefront: free versus chaotic models
- 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 model
- Emergence of caustics in dynamics of the Kitaev model