Tuning towards dynamic freezing using a two-rate protocol

Abstract

We study periodically driven closed quantum systems where two parameters of the system Hamiltonian are driven with frequencies ${\omega }_1$ and ${\omega }_2=r{\omega }_1$. We show that such drives may be used to tune towards dynamics induced freezing where the wavefunction of the state of the system after a drive cycle at time $T=2\pi /{\omega }_1$ has almost perfect overlap with the initial state. We locate regions in the $({\omega }_1,r)$ plane where the freezing is near exact for a class of integrable and a specific non-integrable model. The integrable models that we study encompass Ising and XY models in $d=1$, Kitaev model in $d=2$, and Dirac fermions in graphene and atop a topological insulator surface whereas the non-integrable model studied involves the experimentally realized one-dimensional (1D) tilted Bose-Hubbard model in an optical lattice. In addition, we compute the relevant correlation functions of such driven systems and describe their characteristics in the region of $({\omega }_1,r)$ plane where the freezing is near-exact. We supplement our numerical analysis with semi-analytic results for integrable driven systems within adiabatic-impulse approximation and discuss experiments which may test our theory.

v1: 9 pages 9 figs

References in corpus (47)

• The electronic properties of graphene
• Topological Insulators
• Topological insulators and superconductors
• Anyons in an exactly solved model and beyond
• Electronic transport in two dimensional graphene
• Nonequilibrium dynamics of closed interacting quantum systems
• Electronic Properties of Graphene in a Strong Magnetic Field
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Landau-Zener-Stuckelberg interferometry
• Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
• Universal adiabatic dynamics across a quantum critical point
• Mach-Zehnder Interferometry in a Strongly Driven Superconducting Qubit
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• Theory of finite-entanglement scaling at one-dimensional quantum critical points
• Dynamical Critical Phenomena in Driven-Dissipative Systems
• Quench dynamics across quantum critical points
• Colloquium: Graphene spectroscopy
• 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
• The Kibble-Zurek Problem: Universality and the Scaling Limit
• Defect production in non-linear quench across a quantum critical point
• Mott insulators in strong electric fields
• Exact results for quench dynamics and defect production in a two-dimensional model
• Exotic Freezing of Response in Quantum Many-Body System
• First order dynamical phase transitions
• Slow quenches in a quantum Ising chain; dynamical phase transitions and topology
• Mode coupling induced dissipative and thermal effects at long times after a quantum quench
• Dynamical quantum phase transitions in the axial next-nearest-neighbour Ising chain
• Quench dynamics and defect production in the Kitaev and extended Kitaev models
• Quantum Phase Tomography of a Strongly Driven Qubit
• Freezing a Quantum Magnet by Repeated Quantum Interference: An Experimental Realization
• Thermalization and dissipation in out of equilibrium quantum systems: A perturbative renormalization group approach
• Dynamic freezing of strongly correlated ultracold bosons
• Correlated phases of bosons in tilted, frustrated lattices
• Non-equilibrium dynamics of Bosonic Mott insulators in an electric field
• Microscopic expression for the heat in the adiabatic basis
• Controlling quantum critical dynamics of isolated systems
• Dynamic freezing and defect suppression in the tilted one-dimensional Bose-Hubbard model
• Suppressing defect production during passage through a quantum critical point
• A perturbative renormalization group approach to driven quantum systems
• Statistics of work distribution in periodically driven closed quantum systems
• Cusps in the quench dynamics of a Bloch state
• Frustrated quantum Ising spins simulated by spinless bosons in a tilted lattice: from a quantum liquid to antiferromagnetic order
• Nonsmooth and level-resolved dynamics illustrated with the tight binding model
• Optical Lattice Modulation Spectroscopy for Spin-orbit Coupled Bosons

Cited by in corpus (17)

• Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference
• Dynamics of the vacuum state in a periodically driven Rydberg chain
• Analytic approaches to periodically driven closed quantum systems: Methods and Applications
• Mobility edge and multifractality in a periodically driven Aubry-André model
• Low-frequency phase diagram of irradiated graphene and periodically driven spin-1/2 $XY$ chain
• Ramp and periodic dynamics across non-Ising critical points
• Photo-induced Entanglement in a Magnonic Floquet Topological Insulator
• Emergent symmetries in prethermal phases of periodically driven quantum systems
• Emergent strong zero mode through local Floquet engineering
• Floquet topological transition by unpolarized light
• Driven Hubbard model on a triangular lattice: tunable Heisenberg antiferromagnet with three-spin chiral term
• Many-body localized phase of bosonic dipoles in a tilted optical lattice
• Two rate periodic protocol with dynamics driven through many cycles
• Quantum Oscillation and Landau-Zener transition in Untilted Nodal line semimetals under a time-periodic magnetic field
• Fermi Level Fluctuations, Reduced Effective Masses and Zeeman Effect during Quantum Oscillations in Nodal Line Semimetals
• Chiral anomaly induced magnetoconductances in an irradiated Type-I Weyl Semimetal
• Quantum dynamics of a spin model with an extensive degeneracy