Dynamical relaxation of correlators in periodically driven integrable quantum systems

Abstract

We show that the correlation functions of a class of periodically driven integrable closed quantum systems approach their steady state value as $n^{-(\alpha +1)/\beta }$, where $n$ is the number of drive cycles and $\alpha$ and $\beta$ denote positive integers. We find that generically $\beta =2$ within a dynamical phase characterized by a fixed $\alpha$; however, its value can change to $\beta =3$ or $\beta =4$ either at critical drive frequencies separating two dynamical phases or at special points within a phase. We show that such decays are realized in both driven Su-Schrieffer-Heeger (SSH) and one-dimensional (1D) transverse field Ising models, discuss the role of symmetries of the Floquet spectrum in determining $\beta$, and chart out the values of $\alpha$ and $\beta$ realized in these models. We analyze the SSH model for a continuous drive protocol using a Floquet perturbation theory which provides analytical insight into the behavior of the correlation functions in terms of its Floquet Hamiltonian. This is supplemented by an exact numerical study of a similar behavior for the 1D Ising model driven by a square pulse protocol. For both models, we find a crossover timescale $n_c$ which diverges at the transition. We also unravel a long-time oscillatory behavior of the correlators when the critical drive frequency, ${\omega }_c$, is approached from below ($\omega <{\omega }_c$). We tie such behavior to the presence of multiple stationary points in the Floquet spectrum of these models and provide an analytic expression for the time period of these oscillations.

v1; 16 pages, 8 figs

References in corpus (86)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Nonequilibrium dynamics of closed interacting quantum systems
• Probing many-body dynamics on a 51-atom quantum simulator
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Floquet Topological Insulator in Semiconductor Quantum Wells
• A quantum gas microscope - detecting single atoms in a Hubbard regime optical lattice
• Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
• Topological characterization of periodically-driven quantum systems
• Time-dependence of correlation functions following a quantum quench
• Observation of a Discrete Time Crystal
• Transport properties of non-equilibrium systems under the application of light: Photo-induced quantum Hall insulators without Landau levels
• Floquet Time Crystals
• Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate
• On the phase structure of driven quantum systems
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Probing the Superfluid to Mott Insulator Transition at the Single Atom Level
• Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
• Dynamical quantum phase transitions: a review
• Dynamics of quantum phase transition: exact solution in quantum Ising model
• Quantum Quenches in Extended Systems
• Universal adiabatic dynamics across a quantum critical point
• High-fidelity control and entanglement of Rydberg atom qubits
• The simplest quantum model supporting the Kibble-Zurek mechanism of topological defect production: Landau-Zener transitions from a new perspective
• Quench dynamics across quantum critical points
• Topological singularities and the general classification of Floquet-Bloch systems
• Chiral symmetry and bulk--boundary correspondence in periodically driven one-dimensional systems
• Floquet generation of Majorana end modes and topological invariants
• Breakdown of the adiabatic limit in low dimensional gapless systems
• Supplementary Information to the paper ``Breakdown of the adiabatic limit in low dimensional gapless systems''
• Many-body energy localization transition in periodically driven systems
• Dynamical phase transitions after quenches in non-integrable models
• Dynamical quantum phase transitions: scaling and universality
• Dynamical quantum phase transitions and the Loschmidt echo: A transfer matrix approach
• Quench dynamics near a quantum critical point
• Effective Theory of Floquet Topological Transitions
• Defect production in non-linear quench across a quantum critical point
• Exact results for quench dynamics and defect production in a two-dimensional model
• Entropy and Correlation Functions of a Driven Quantum Spin Chain
• Quantum phase transitions in transverse field spin models: from statistical physics to quantum information
• Exotic Freezing of Response in Quantum Many-Body System
• Collapse and revival of quantum many-body scars via Floquet engineering
• Floquet Topological States in Shaking Optical Lattices
• First order dynamical phase transitions
• Slow quenches in a quantum Ising chain; dynamical phase transitions and topology
• Dynamical quantum phase transitions in the axial next-nearest-neighbour Ising chain
• Quench dynamics and defect production in the Kitaev and extended Kitaev models
• Quenching along a gapless line: A different exponent for defect density
• Long-lived interacting phases of matter protected by multiple time-translation symmetries in quasiperiodically-driven systems
• Logarithmically Slow Relaxation in Quasi-Periodically Driven Random Spin Chains
• Dynamics of the vacuum state in a periodically driven Rydberg chain
• Dynamical localization in a chain of hard core bosons under a periodic driving
• Transverse Ising Chain under Periodic Instantaneous Quenches: Dynamical Many-Body Freezing and Emergence of Solitary Oscillation
• Entanglement generation in periodically driven integrable systems: dynamical phase transitions and steady state
• Defect production due to quenching through a multicritical point
• Freezing a Quantum Magnet by Repeated Quantum Interference: An Experimental Realization
• Random multipolar driving: tunably slow heating through spectral engineering
• Non-equilibrium dynamics of the Bose-Hubbard model: A projection operator approach
• Aperiodically driven integrable systems and their emergent steady states
• Theory of defect production in nonlinear quench across a quantum critical point
• Absence of dynamical localization in interacting driven systems
• Analytic approaches to periodically driven closed quantum systems: Methods and Applications
• Quasi-periodically driven quantum systems
• Population dynamics in Floquet realisation of Harper-Hofstadter Hamiltonian
• Defect generation in a spin-1/2 transverse XY chain under repeated quenching of the transverse field
• Effects of interactions on periodically driven dynamically localized systems
• Restoring coherence via aperiodic drives in a many-body quantum system
• Effects of periodic kicking on dispersion and wave packet dynamics in graphene
• Dynamic freezing of strongly correlated ultracold bosons
• Observing Dynamical Quantum Phase Transitions through Quasilocal String Operators
• Long-lived period-doubled edge modes of interacting and disorder-free Floquet spin chains
• Dynamical freezing of relaxation to equilibrium
• Maximum group velocity in a one-dimensional model with a sinusoidally varying staggered potential
• Low-frequency phase diagram of irradiated graphene and periodically driven spin-1/2 $XY$ chain
• Nonadiabatic charge pumping by oscillating potentials in one dimension: results for infinite system and finite ring
• Dynamic freezing and defect suppression in the tilted one-dimensional Bose-Hubbard model
• Periodically driven integrable systems with long-range pair potentials
• Robustness of symmetry-protected topological states against time-periodic perturbations
• Steady states of a quasiperiodically driven integrable system
• Dynamics of quasiperiodically driven spin systems
• Signatures and conditions for phase band crossings in periodically driven integrable systems
• (Quasi)Periodic revivals in periodically driven interacting quantum systems
• A Floquet perturbation theory for periodically driven weakly-interacting fermions
• Dynamical crossover behavior in the relaxation of quenched quantum many-body systems
• Dynamical Transition for a class of integrable models coupled to a bath
• Transport signatures of symmetry protection in 1D Floquet topological insulators

Cited by in corpus (18)

• Dynamical crossover behavior in the relaxation of quenched quantum many-body systems
• Periodically driven Rydberg chains with staggered detuning
• Out-of-Time-Order correlators in driven conformal field theories
• Krylov complexity and Trotter transitions in unitary circuit dynamics
• Periodically driven model with quasiperiodic potential and staggered hopping amplitudes: engineering of mobility gaps and multifractal states
• Hinge mode dynamics of periodically driven higher-order Weyl semimetals
• Emergent conservation in Floquet dynamics of integrable non-Hermitian models
• Dynamical localization and slow thermalization in a class of disorder-free periodically driven one-dimensional interacting systems
• Dynamical relaxation behaviors of a critical quench
• Entanglement transitions in a periodically driven non-Hermitian Ising chain
• Dynamic generation of nonequilibrium superconducting states in Kitaev chain
• Entanglement in quenched extended Su-Schrieffer-Heeger model with anomalous dynamical quantum phase transitions
• Exploring Dynamical Phase Transitions in the XY Chain through Linear Quench: Early and Long-term Perspectives
• Dynamical relaxation behavior of extended XY chain with gapless phase following a quantum quench
• Insights from the exact analytical solution of periodically driven transverse field Ising chain
• Su-Schrieffer-Heeger model driven by sequences of two unitaries: periodic, quasiperiodic, aperiodic, and random protocols
• Slow decay rate of correlations induced by long-range extended Dzyaloshinskii-Moriya interactions
• Relaxation dynamics in the alternating XY chain following a quantum quench