Nonequilibrium dynamics of the Ising chain in a fluctuating transverse field

Abstract

We study nonequilibrium dynamics of the quantum Ising chain at zero temperature when the transverse field is varied stochastically. In the equivalent fermion representation, the equation of motion of Majorana operators is derived in the form of a one-dimensional, continuous-time quantum random walk with stochastic, time-dependent transition amplitudes. This type of external noise gives rise to decoherence in the associated quantum walk and the semiclassical wave-packet generally has a diffusive behavior. As a consequence, in the quantum Ising chain, the average entanglement entropy grows in time as $t^{1/2}$ and the logarithmic average magnetization decays in the same form. In the case of a dichotomous noise, when the transverse-field is changed in discrete time-steps, $\tau$, there can be excitation modes, for which coherence is maintained, provided their energy satisfies ${\epsilon }_k\tau \approx n\pi$ with a positive integer $n$. If the dispersion of ${\epsilon }_k$ is quadratic, the long-time behavior of the entanglement entropy and the logarithmic magnetization is dominated by these ballistically traveling coherent modes and both will have a $t^{3/4}$ time-dependence.

12 pages, 10 figures

References in corpus (63)

• Many-Body Physics with Ultracold Gases
• Thermalization and its mechanism for generic isolated quantum systems
• Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Quantum Quench in the Transverse Field Ising Chain
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• The Luttinger model following a sudden interaction switch-on
• Universal adiabatic dynamics across a quantum critical point
• Exact relaxation in a class of non-equilibrium quantum lattice systems
• Dephasing and the steady state in quantum many-particle systems
• Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
• Strong and weak thermalization of infinite non-integrable quantum systems
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
• Quench dynamics across quantum critical points
• Strongly correlated fermions after a quantum quench
• Quantum quench dynamics of the Luttinger model
• Absence of Thermalization in Nonintegrable Systems
• Supplementary Information to the paper ``Breakdown of the adiabatic limit in low dimensional gapless systems''
• Breakdown of the adiabatic limit in low dimensional gapless systems
• Effective thermal dynamics following a quantum quench in a spin chain
• Decoherence in quantum walks - a review
• Defect production in non-linear quench across a quantum critical point
• Quantum Quench in the Transverse Field Ising Chain II: Stationary State Properties
• Exact results for quench dynamics and defect production in a two-dimensional model
• Dynamical Correlations after a Quantum Quench
• Evolution of entanglement after a local quench
• Topology induced anomalous defect production by crossing a quantum critical point
• Long time dynamics following a quench in an integrable quantum spin chain: local versus non-local operators and effective thermal behavior
• Quenching Dynamics of a quantum XY spin-1/2 chain in presence of a transverse field
• Quantum quenches in a spinor condensate
• Quantum Quenches, Thermalization and Many-Body Localization
• Adiabatic quantum dynamics of a random Ising chain across its quantum critical point
• Relaxation of a one-dimensional Mott insulator after an interaction quench
• Quasilocal conserved operators in isotropic Heisenberg spin 1/2 chain
• Quantum quench dynamics of the sine-Gordon model in some solvable limits
• Exploring local quantum many-body relaxation by atoms in optical superlattices
• Thermalization and Revivals after a Quantum Quench in Conformal Field Theory
• Optimal non-linear passage through a quantum critical point
• Quantum Quench from a Thermal Initial State
• Dynamics in the Ising field theory after a quantum quench
• Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined
• Quantum Walks on a Random Environment
• Quenching the XXZ spin chain: quench action approach versus generalized Gibbs ensemble
• Quantum relaxation after a quench in systems with boundaries
• Adiabatic dynamics in open quantum critical many-body systems
• Dynamical non-ergodic scaling in continuous finite-order quantum phase transitions
• Dynamical Stability of a Many-body Kapitza Pendulum
• Quench dynamics and defect production in the Kitaev and extended Kitaev models
• Quenching along a gapless line: A different exponent for defect density
• Exact infinite-time statistics of the Loschmidt echo for a quantum quench
• Entanglement evolution after connecting finite to infinite quantum chains
• Entanglement in a periodic quench
• Entanglement Routers Using Macroscopic Singlets
• Defect production due to quenching through a multicritical point
• Finite-size corrections vs. relaxation after a sudden quench
• Theory of defect production in nonlinear quench across a quantum critical point
• Failure of the Generalized Eigenstate Thermalization Hypothesis in integrable models with multiple particle species
• Quantum quenches and Generalized Gibbs Ensemble in a Bethe Ansatz solvable lattice model of interacting bosons
• Quantum versus classical annealing: insights from scaling theory and results for spin glasses on 3-regular graphs
• Adiabatic nonlinear probes of one-dimensional Bose gases
• Adiabatic multicritical quantum quenches: Continuously varying exponents depending on the direction of quenching

Cited by in corpus (10)

• Quantum Entanglement Growth Under Random Unitary Dynamics
• Emergent conformal symmetry in non-unitary random dynamics of free fermions
• Aperiodically driven integrable systems and their emergent steady states
• Steady states of a quasiperiodically driven integrable system
• Fibonacci steady states in a driven integrable quantum system
• The non-stabilizerness of fermionic Gaussian states
• Controlling measurement-induced phase transitions with tunable detector coupling
• Matchgate circuits deeply thermalize
• Su-Schrieffer-Heeger model driven by sequences of two unitaries: periodic, quasiperiodic, aperiodic, and random protocols
• Fourier Neural Operators for Time-Periodic Quantum Systems: Learning Floquet Hamiltonians, Observable Dynamics, and Operator Growth