Ramp and periodic dynamics across non-Ising critical points

Abstract

We study ramp and periodic dynamics of ultracold bosons in an one-dimensional (1D) optical lattice which supports quantum critical points separating a uniform and a $Z_3$ or $Z_4$ symmetry broken density-wave ground state. Our protocol involves both linear and periodic drives which takes the system from the uniform state to the quantum critical point (for linear drive protocol) or to the ordered state and back (for periodic drive protocols) via controlled variation of a parameter of the system Hamiltonian. We provide exact numerical computation, for finite-size boson chains with $L\le 24$ using exact-diagonalization (ED), of the excitation density $D$, the wavefunction overlap $F$, and the excess energy $Q$ at the end of the drive protocol. For the linear ramp protocol, we identify the range of ramp speeds for which $D$ and $Q$ shows Kibble-Zurek scaling. We find, based on numerical analysis with $L\le 24$, that such scaling is consistent with that expected from critical exponents of the $q$-state Potts universality class with $q=3,4$. For periodic protocol, we show that the model display near-perfect dynamical freezing at specific frequencies; at these frequencies $D,Q\to 0$ and $|F|\to 1$. We provide a semi-analytic explanation of such freezing behavior and relate this phenomenon to a many-body version of Stuckelberg interference. We suggest experiments which can test our theory.

v2,final version accepeted in PRB

References in corpus (23)

• 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
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Landau-Zener-Stuckelberg interferometry
• Probing the Superfluid to Mott Insulator Transition at the Single Atom Level
• Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
• Quench dynamics across quantum critical points
• Competing density-wave orders in a one-dimensional hard-boson model
• Mott insulators in strong electric fields
• Exotic Freezing of Response in Quantum Many-Body System
• Ashkin-Teller criticality and pseudo first-order behavior in a frustrated Ising model on the square lattice
• Universal nonequilibrium quantum dynamics in imaginary time
• 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
• Dynamic freezing and defect suppression in the tilted one-dimensional Bose-Hubbard model
• Resonantly Enhanced Tunneling and Transport of Ultracold Atoms on Tilted Optical Lattices
• Many-body Landau-Zener tunneling in the Bose-Hubbard model
• "Bloch oscillations" in the Mott-insulator regime
• Tuning towards dynamic freezing using a two-rate protocol
• Frustrated quantum Ising spins simulated by spinless bosons in a tilted lattice: from a quantum liquid to antiferromagnetic order

Cited by in corpus (14)

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• Numerical study of the chiral ${\mathbb{Z}}_3$ quantum phase transition in one spatial dimension
• Restoring coherence via aperiodic drives in a many-body quantum system
• Diagnosing Potts criticality and two-stage melting in one-dimensional hard-boson models
• Varying quench dynamics in the transverse Ising chain: the Kibble-Zurek, saturated, and pre-saturated regimes
• Quantum order-by-disorder induced phase transition in Rydberg ladders with staggered detuning
• Nonequilibrium critical dynamics in the quantum chiral clock model
• Many-body localized phase of bosonic dipoles in a tilted optical lattice
• Post quench entropy growth in a chiral clock model
• Exploring quantum criticality and ergodicity-breaking dynamics in spin-1 Kitaev chains via single-ion anisotropies
• Scaling of Loschmidt echo in boundary driven critical Z-3 Potts model
• Detecting prethermal Floquet phases of Rydberg atom arrays
• Quantum dynamics of a spin model with an extensive degeneracy