Kibble-Zurek Mechanism and Finite-Time Scaling

Abstract

The Kibble-Zurek (KZ) mechanism has been applied to a variety of systems ranging from low temperature Bose-Einstein condensations to grand unification scales in particle physics and cosmology and from classical phase transitions to quantum phase transitions. Here we show that finite-time scaling (FTS) provides a detailed improved understanding of the mechanism. In particular, the finite time scale, which is introduced by the external driving (or quenching) and results in FTS, is the origin of the division of the adiabatic regimes from the impulse regime in the KZ mechanism. The origin of the KZ scaling for the defect density, generated during the driving through a critical point, is not that the correlation length ceases growing in the nonadiabatic impulse regime, but rather, is that it is taken over by the effective finite length scale corresponding to the finite time scale. We also show that FTS accounts well for and improves the scaling ansatz proposed recently by Liu, Polkovnikov, and Sandvik [Phys. Rev. B {\bf 89}, 054307 (2014)]. Further, we show that their universal power-law scaling form applies only to some observables in cooling but not to heating. Even in cooling, it is invalid either when an appropriate external field is present. However, this finite-time-finite-size scaling calls for caution in application of FTS. Detailed scaling behaviors of the FTS and finite-size scaling, along with their crossover, are explicitly demonstrated, with the dynamic critical exponent $z$ being estimated for two- and three-dimensional Ising models under the usual Metropolis dynamics. These values of $z$ are found to give rise to better data collapses than the extant values do in most cases but take on different values in heating and cooling in both two- and three-dimensional spaces.

14 pages, 14 figures

References in corpus (7)

• Universal adiabatic dynamics across a quantum critical point
• Universality of Phase Transition Dynamics: Topological Defects from Symmetry Breaking
• Defect production in non-linear quench across a quantum critical point
• Topology induced anomalous defect production by crossing a quantum critical point
• Structural defects in ion crystals by quenching the external potential: the inhomogeneous Kibble-Zurek mechanism
• Dynamics of a quantum phase transition in a ferromagnetic Bose-Einstein condensate
• Dynamical non-ergodic scaling in continuous finite-order quantum phase transitions

Cited by in corpus (39)

• Nonequilibrium dynamics of the localization-delocalization transition in the non-Hermitian Aubry-André model
• Kibble-Zurek scaling in the Yang-Lee edge singularity
• Theory of Driven Nonequilibrium Critical Phenomena
• Universal driven critical dynamics across a quantum phase transition in ferromagnetic spinor atomic Bose-Einstein condensates
• Kibble-Zurek mechanism in the Ising Field Theory
• Activating critical exponent spectra with a slow drive
• Scaling of the entanglement spectrum in driving critical dynamics
• Hybridized Kibble-Zurek scaling in the driven critical dynamics across an overlapping critical region
• Emergent Coulombic criticality and Kibble-Zurek scaling in a topological magnet
• Kibble-Zurek mechanism beyond adiabaticity: Finite-time scaling with critical initial slip
• Kibble-Zurek mechanism in a one-dimensional incarnation of deconfined quantum critical point
• Renormalization-group theory for cooling first-order phase transitions in Potts models
• Quantum criticality and Kibble-Zurek scaling in the Aubry-André-Stark model
• Dynamical off-equilibrium scaling across magnetic first-order phase transitions
• Scaling Theories of Kosterlitz-Thouless Phase Transitions
• Scaling theory of entanglement entropy in confinements near quantum critical points
• Driving Driven Lattice Gases to Identify Their Universality Classes
• Dynamical Ginzburg criterion for the quantum-classical crossover of the Kibble-Zurek mechanism
• Resolving chiral transitions in Rydberg arrays with quantum Kibble-Zurek mechanism and finite-time scaling
• Kibble-Zurek scaling in one-dimensional localization transitions
• Spin Glass in the Bond-Diluted J1-J2 Ising Model on the Square Lattice
• Self-similarity breaking: Anomalous nonequilibrium finite-size scaling and finite-time scaling
• Equilibration of Topological Defects Near the Deconfined Quantum Multicritical Point
• Finite-time scaling beyond the Kibble-Zurek prerequisite in Dirac systems
• Tricritical Kibble-Zurek scaling in Rydberg atom ladders
• Universal imaginary-time critical dynamics on a quantum computer
• Complete universal scaling in first-order phase transitions
• Universal scaling in first-order phase transitions mixed with nucleation and growth
• Non-equilibrium dynamics of localization phase transition in the non-Hermitian Disorder-Aubry-André model
• Nonequilibrium Critical Dynamics with Emergent Supersymmetry
• Theory of Critical Phenomena with Long-Range Temporal Interaction
• Theory of Critical Phenomena with Memory
• Driven Critical Dynamics in Tricitical Point
• Is there Kibble-Zurek scaling of topological defects in first-order phase transitions?
• Scaling corrections in driven critical dynamics: Application to a two-dimensional dimerized quantum Heisenberg model
• Complete universal scaling of first-order phase transitions in the two-dimensional Ising model
• Finite-time scaling with two characteristic time scales: Driven critical dynamics with emergent symmetry
• Anomalous Dynamical Scaling at Topological Quantum Criticality
• Unifying Kibble-Zurek Mechanism in Weakly Driven Processes