Entropy of entanglement and correlations induced by a quench: Dynamics of a quantum phase transition in the quantum Ising model

Abstract

Quantum Ising model in one dimension is an exactly solvable example of a quantum phase transition. We investigate its behavior during a quench from a paramagnetic to ferromagnetic phase caused by a gradual turning off of the transverse field at a fixed rate characterized by the quench time ${\tau }_Q$. In agreement with Kibble-Zurek mechanism, quantum state of the system after the transition exhibits a characteristic correlation length $\hat{\xi }$ proportional to the square root of the quench time ${\tau }_Q$. The inverse of this correlation length determines average density of defects after the transition. In this paper, we show that $\hat{\xi }$ also controls the entropy of entanglement of a block of $L$ spins with the rest of the system. For large $L$, this entropy saturates at $\frac{1}{6}{\log }_2\hat{\xi }$, as might have been expected from the Kibble-Zurek mechanism. Close to the critical point, the entropy saturates when the block size $L\approx \hat{\xi }$, but -- in the subsequent evolution in the ferromagnetic phase -- a somewhat larger length scale $l=\sqrt{{\tau }_Q}\ln {\tau }_Q$ develops as a result of quantum dephasing, and the entropy saturates when $L\approx l$. We also study the spin-spin correlation. We find that close to the critical point ferromagnetic correlations decay exponentially with the dynamical correlation length $\hat{\xi }$, but in the following evolution this correlation function becomes oscillatory at distances less than this scale. However, both the wavelength and the correlation length of these oscillations are still determined by $\hat{\xi }$. We also derive probability distribution for the number of kinks in a finite spin chain after the transition.

arXiv comment12 pages, 3 figures; updated references and minor cosmetic changes

References in corpus (39)

• Entanglement in quantum critical phenomena
• Efficient classical simulation of slightly entangled quantum computations
• Efficient simulation of one-dimensional quantum many-body systems
• Geometric and Renormalized Entropy in Conformal Field Theory
• Time-dependence of correlation functions following a quantum quench
• Cosmological Experiments in Condensed Matter Systems
• Dynamics of a Quantum Phase Transition
• Dynamics of quantum phase transition: exact solution in quantum Ising model
• Big bang simulation in superfluid 3He-B -- Vortex nucleation in neutron-irradiated superflow
• Universal adiabatic dynamics across a quantum critical point
• Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
• The Cosmological Kibble Mechanism in the Laboratory: String Formation in Liquid Crystals
• The simplest quantum model supporting the Kibble-Zurek mechanism of topological defect production: Landau-Zener transitions from a new perspective
• Entanglement entropy of random quantum critical points in one dimension
• Quench dynamics across quantum critical points
• Entanglement in XY Spin Chain
• Density of kinks after a quench: When symmetry breaks, how big are the pieces?
• Observation of Magnetic Flux Generated Spontaneously During a Rapid Quench of Superconducting Films
• Entropy and Correlation Functions of a Driven Quantum Spin Chain
• Adiabatic-Impulse approximation for avoided level crossings: from phase transition dynamics to Landau-Zener evolutions and back again
• Long range correlations in the non-equilibrium quantum relaxation of a spin chain
• Scaling of Entanglement Entropy in the Random Singlet Phase
• Zurek-Kibble domain structures: The Dynamics of Spontaneous Vortex formation in Annular Josephson Tunnel Junctions
• Non-Appearance of Vortices in Fast Mechanical Expansions of Liquid 4He Through the Lambda Transition
• Vortex String Formation in a 3D U(1) Temperature Quench
• Symmetry Breaking with a Slant: Topological Defects after an Inhomogeneous Quench
• Vortex formation in two dimensions: When symmetry breaks, how big are the pieces?
• Defect formation and local gauge invariance
• Dynamics of the Bose-Hubbard model: transition from Mott insulator to superfluid
• Dynamics of a quantum phase transition in the random Ising model
• Zurek-Kibble Mechanism for the Spontaneous Vortex Formation in $Nb-Al/A{l}_{ox}/Nb$ Josephson Tunnel Junctions: New Theory and Experiment
• Winding up by a quench: vortices in the wake of rapid Bose-Einstein condensation
• Critical Dynamics of Symmetry Breaking: Quenches, Dissipation and Cosmology
• Asymptotics of Toeplitz Determinants and the Emptiness Formation Probability for the XY Spin Chain
• Applications and generalizations of Fisher-Hartwig asymptotics
• Dynamics of Quantum Phase Transition in an Array of Josephson Junctions
• Spontaneous Fluxon Formation in Annular Josephson Tunnel Junctions
• Defect Formation and Critical Dynamics in the Early Universe
• Critical dynamics of gauge systems: Spontaneous vortex formation in 2D superconductors

Cited by in corpus (131)

• Nonequilibrium dynamics of closed interacting quantum systems
• Entanglement entropy and conformal field theory
• Reduced density matrices and entanglement entropy in free lattice models
• Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
• Quantum Quenches in Extended Systems
• Entanglement and correlation functions following a local quench: a conformal field theory approach
• Discovering Phases, Phase Transitions and Crossovers through Unsupervised Machine Learning: A critical examination
• Universality of Phase Transition Dynamics: Topological Defects from Symmetry Breaking
• Holographic Evolution of Entanglement Entropy
• Quantum discord and its allies: a review
• A short review on entanglement in quantum spin systems
• Quenching Dynamics of a quantum XY spin-1/2 chain in presence of a transverse field
• Adiabatic quantum dynamics of a random Ising chain across its quantum critical point
• Non-equilibrium dynamic critical scaling of the quantum Ising chain
• Dynamics after a sweep through a quantum critical point
• Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond
• Beyond-classical computation in quantum simulation
• Adiabatic dynamics in open quantum critical many-body systems
• Quantum quench in a p + i p superfluid: Winding numbers and topological states far from equilibrium
• Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model
• Quantum phase transition dynamics in the two-dimensional transverse-field Ising model
• Out of equilibrium dynamics with Matrix Product States
• Coherent and dissipative dynamics at quantum phase transitions
• Causality and non-equilibrium second-order phase transitions in inhomogeneous systems
• Space-time renormalization in phase transition dynamics
• Dynamics of entanglement entropy and entanglement spectrum crossing a quantum phase transition
• Entanglement in a periodic quench
• Critical Phenomena and Kibble-Zurek Scaling in the Long-Range Quantum Ising Chain
• Entanglement generation in periodically driven integrable systems: dynamical phase transitions and steady state
• Work distribution and edge singularities for generic time-dependent protocols in extended systems
• Dynamics of an inhomogeneous quantum phase transition
• Adiabatic quenches through an extended quantum critical region
• Time evolution of 1D gapless models from a domain-wall initial state: SLE continued?
• Symmetry breaking bias and the dynamics of a quantum phase transition
• Kibble-Zurek mechanism with a single particle: dynamics of the localization-delocalization transition in the Aubry-André model
• Dynamics of the entanglement spectrum in spin chains
• New dynamical scaling universality for quantum networks across adiabatic quantum phase transitions
• Growth of mutual information in a quenched one-dimensional open quantum many body system
• Exploiting Quench Dynamics in Spin Chains for Distant Entanglement and Quantum Communication
• Dynamics of a quantum phase transition in the 1D Bose-Hubbard model: excitations and correlations induced by a quench
• Phase Transition in Space: How Far Does a Symmetry Bend Before It Breaks?
• Correlation dynamics during a slow interaction quench in a one-dimensional Bose gas
• Sonic horizons and causality in the phase transition dynamics
• Entanglement production due to quench dynamics of an anisotropic XY chain in a transverse field
• Quantum Quench and Scaling of Entanglement Entropy
• Non-equilibrium dynamics of quantum systems: order parameter evolution, defect generation, and qubit transfer
• Von Neumann Entropy Spectra and Entangled Excitations in Spin-Orbital Models
• Spin and topological order in a periodically driven spin chain
• Multipartite entanglement after a quantum quench
• Decoherence in the dynamical quantum phase transition of the transverse Ising chain
• Kibble-Zurek Dynamics in a Trapped Ultracold Bose Gas
• Dynamical structure factors of dynamical quantum simulators
• Universal energy distribution of quasi-particles emitted in a local time dependent quench
• Quantum phase transition in space in a ferromagnetic spin-1 Bose-Einstein condensate
• Quantum Critical Scaling under Periodic Driving
• Distribution of Kinks in an Ising Ferromagnet After Annealing and the Generalized Kibble-Zurek Mechanism
• Quantum quench spectroscopy of a Luttinger liquid: Ultrarelativistic density wave dynamics due to fractionalization in an XXZ chain
• Benchmarking digital quantum simulations above hundreds of qubits using quantum critical dynamics
• Entanglement entropy in a periodically driven Ising chain
• Kibble-Zurek mechanism in the Ising Field Theory
• Quantum criticality using a superconducting quantum processor
• Adiabatic preparation without Quantum Phase Transitions
• Quantum Kibble-Zurek mechanism: Kink correlations after a quench in the quantum Ising chain
• Quench from Mott Insulator to Superfluid
• Topological defect formation in a phase transition with tunable order
• Observing a Quantum Phase Transition by Measuring a Single Spin
• Adiabatic dynamics of an inhomogeneous quantum phase transition: the case of z > 1 dynamical exponent
• Locality of Spontaneous Symmetry Breaking and Universal Spacing Distribution of Topological Defects Formed Across a Phase Transition
• Scaling of the entanglement spectrum in driving critical dynamics
• Time Evolution of an Infinite Projected Entangled Pair State: an Algorithm from First Principles
• Coherent Many-Body Oscillations Induced by a Superposition of Broken Symmetry States in the Wake of a Quantum Phase Transition
• Dynamics of a quantum phase transition with decoherence: the quantum Ising chain in a static spin environment
• Varying quench dynamics in the transverse Ising chain: the Kibble-Zurek, saturated, and pre-saturated regimes
• Driven quantum spin chain in the presence of noise: Anti-Kibble-Zurek behavior
• How to fix a broken symmetry: Quantum dynamics of symmetry restoration in a ferromagnetic Bose-Einstein condensate
• Dynamics of longitudinal magnetization in transverse-field quantum Ising model: from symmetry-breaking gap to Kibble-Zurek mechanism
• Entanglement entropy in a periodically driven quantum Ising chain
• Locating quantum critical points with Kibble-Zurek quenches
• Entanglement dynamics in the three-dimensional Anderson model
• Phase boundaries in alternating field quantum XY model with Dzyaloshinskii-Moriya interaction: Sustainable entanglement in dynamics
• Tensor network simulation of the quantum Kibble-Zurek quench from the Mott to superfluid phase in the two-dimensional Bose-Hubbard model
• Quantum Quench in Non-relativistic Fermionic Field Theory: Harmonic traps and 2d String Theory
• Quenching Dynamics and Quantum Information
• Magnetic field dependence of the entanglement entropy of one dimensional spin systems in quantum phase transition induced by a quench
• Large Deviations Beyond the Kibble-Zurek Mechanism
• Role of boundary conditions in the full counting statistics of topological defects after crossing a continuous phase transition
• Kink correlations, domain size distribution, and the emptiness formation probability after the Kibble-Zurek quench in the quantum Ising chain
• Stable topological textures in a classical 2D Heisenberg model
• Eigenstate entanglement in integrable collective spin models
• Scaling theory of entanglement entropy in confinements near quantum critical points
• Exact thermal properties of free-fermionic spin chains
• Interferometry based on quantum Kibble-Zurek mechanism
• Exact results for the criticality of quench dynamics in quantum Ising models
• Quench Dynamics of Entanglement in an Opened Anisotropic Spin-1/2 Heisenberg Chain
• Scaling in driven dynamics starting in the vicinity of a quantum critical point
• Density of defects and the scaling law of the entanglement entropy in quantum phase transition of one dimensional spin systems induced by a quench
• Survival of time-evolved correlations depends on whether quenching is across critical point in XY spin chain
• Inhomogeneity induced shortcut to adiabaticity in Ising chains with long-range interactions
• Adiabatic dynamics in a spin-1 chain with uniaxial single-spin anisotropy
• Correspondence between Entanglement Growth and Probability Distribution of Quasi-Particles
• Driven one-dimensional noisy Kitaev chain
• Non-Hermitian Quantum Annealing in the Antiferromagnetic Ising Chain
• Quench dynamics of topological quantum phase transition in Wen-plaquette model
• Driving a Quantum Phase Transition at Arbitrary Rate: Exact solution of the Transverse-Field Ising model
• Generation of concurrence between two qubits locally coupled to a one dimensional spin chain
• Biased dynamics of the miscible-immiscible quantum phase transition in a binary Bose-Einstein condensate
• Decoherence of Bell states by local interactions with a suddenly quenched spin environment
• Navigating the noise-depth tradeoff in adiabatic quantum circuits
• The Kibble Zurek Mechanism of Topological Defect Formation in Quantum Field Theory with Matrix Product States
• On the Dynamics of XY Spin Chains with Impurities
• Inhomogeneous adiabatic preparation of a quantum critical ground state in two dimensions
• Quasiadiabatic dynamics of ultracold bosonic atoms in a one-dimensional optical superlattice
• Defect production in quench from current-carrying non-equilibrium state
• Kibble-Zurek scaling in the quantum Ising chain with a time-periodic perturbation
• The geometric phase and the dynamics of quantum phase transition induced by a linear quench
• Driven Critical Dynamics in Tricitical Point
• Kibble-Zurek mechanism and errors of gapped quantum phases
• Entanglement generation and scaling from noisy quenches across a quantum critical point
• The singularities of the rate function of quantum coherent work in one-dimensional transverse field Ising model
• Kibble-Zurek dynamics in the anisotropic Ising model of the Si(001) surface
• Dynamics of the order parameter in symmetry breaking phase transitions
• Dynamics of quantum Fisher and Wigner-Yanase skew information following a noisy quench
• Deconstructing symmetry breaking dynamics
• Quench in 1D Bose-Hubbard Model: Topological Defects and Excitations from Kosterlitz-Thouless Phase Transition Dynamics
• Dynamics of the Mott Insulator to Superfluid quantum phase transition in the truncated Wigner approximation
• Dynamics for the Haldane phase in the Bilinear-Biquadratic Model
• Persistent oscillation of a Cooper-pair condensate of topological defects in a nonintegrable quantum Ising chain
• Quantum cluster kink and ring frustration
• Coexistence of different scaling laws for the entanglement entropy in a periodically driven system
• Entanglement Spreading and Oscillation
• Multipartite Entanglement in Crossing the Quantum Critical Point