Nonequilibrium critical dynamics in the quantum chiral clock model

Abstract

In this paper we study the driven critical dynamics in the three-state quantum chiral clock model. This is motivated by a recent experiment, which verified the Kibble-Zurek mechanism and the finite-time scaling in a reconfigurable one-dimensional array of ${}^{87}$Rb atoms with programmable interactions. This experimental model shares the same universality class with the quantum chiral clock model and has been shown to possess a nontrivial non-integer dynamic exponent $z$. Besides the case of changing the transverse field as realized in the experiment, we also consider the driven dynamics under changing the longitudinal field. For both cases, we verify the finite-time scaling for a non-integer dynamic exponent $z$. Furthermore, we determine the critical exponents $\beta$ and $\delta$ numerically for the first time. We also investigate the dynamic scaling behavior including the thermal effects, which are inevitably involved in experiments. From a nonequilibrium dynamic point of view, our results strongly support that there is a direct continuous phase transition between the ordered phase and the disordered phase. Also, we show that the method based on the finite-time scaling theory provides a promising approach to determine the critical point and critical properties.

8 pages, 7 figures, 1 table

References in corpus (54)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• 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
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Continuous Quantum Phase Transitions
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Quantum many-body scars
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Dynamics of a Quantum Phase Transition
• Matrix product states represent ground states faithfully
• Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
• Dynamics of quantum phase transition: exact solution in quantum Ising model
• Quantum Kibble-Zurek mechanism and critical dynamics on a programmable Rydberg simulator
• Universal adiabatic dynamics across a quantum critical point
• Quantum scarred eigenstates in a Rydberg atom chain: entanglement, breakdown of thermalization, and stability to perturbations
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• Parafermionic edge zero modes in Z_n-invariant spin chains
• Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain
• Topological phases with parafermions: theory and blueprints
• Variational optimization algorithms for uniform matrix product states
• Competing density-wave orders in a one-dimensional hard-boson model
• Signatures of integrability in the dynamics of Rydberg-blockaded chains
• The Kibble-Zurek Problem: Universality and the Scaling Limit
• Quench dynamics near a quantum critical point
• Defect production in non-linear quench across a quantum critical point
• Mott insulators in strong electric fields
• Soliton creation during a Bose-Einstein condensation
• Non-equilibrium dynamic critical scaling of the quantum Ising chain
• Dynamics of a quantum phase transition in a ferromagnetic Bose-Einstein condensate
• Diagonalizing transfer matrices and matrix product operators: a medley of exact and computational methods
• Numerical study of the chiral ${\mathbb{Z}}_3$ quantum phase transition in one spatial dimension
• Dynamical non-ergodic scaling in continuous finite-order quantum phase transitions
• Universal nonequilibrium quantum dynamics in imaginary time
• Stability of zero modes in parafermion chains
• Quench dynamics near a quantum critical point: application to the sine-Gordon model
• Space-time renormalization in phase transition dynamics
• Quantum field theory for the chiral clock transition in one spatial dimension
• Phase diagram of the $Z_3$ Parafermionic Chain with Chiral Interactions
• Floating phase versus chiral transition in a 1D hard-boson model
• Quantum versus classical annealing: insights from scaling theory and results for spin glasses on 3-regular graphs
• Non-equilibrium dynamics of Bosonic Mott insulators in an electric field
• Z4 parafermions in one-dimensional fermionic lattices
• Dynamical critical scaling and effective thermalization in quantum quenches: the role of the initial state
• Domain Formation: Decided Before, or After the Transition?
• Non-topological parafermions in a one-dimensional fermionic model with even multiplet pairing
• Scaling of the entanglement spectrum in driving critical dynamics
• Ramp and periodic dynamics across non-Ising critical points
• Kibble-Zurek scaling of the one-dimensional Bose-Hubbard model at finite temperatures
• Scaling theory of entanglement entropy in confinements near quantum critical points
• Scaling in driven dynamics starting in the vicinity of a quantum critical point

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