Kibble-Zurek mechanism beyond adiabaticity: Finite-time scaling with critical initial slip

Abstract

The Kibble-Zurek mechanism demands an initial adiabatic stage before an impulse stage to have a frozen correlation length that generates topological defects in a cooling phase transition. Here we study such a driven critical dynamics but with an initial condition that is near the critical point and that is far away from equilibrium. In this case, there is no initial adiabatic stage at all and thus adiabaticity is broken. However, we show that there again exists a finite length scale arising from the driving that divides the evolution into three stages. A relaxation--finite-time scaling--adiabatic scenario is then proposed in place of the adiabatic--impulse--adiabatic scenario of the original Kibble-Zurek mechanism. A unified scaling theory, which combines finite-time scaling with critical initial slip, is developed to describe the universal behavior and is confirmed with numerical simulations of a two-dimensional classical Ising model.

5+ε pages, 5 figures

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Cited by in corpus (11)

• Theory of Driven Nonequilibrium Critical Phenomena
• Renormalization-group theory for cooling first-order phase transitions in Potts models
• Scaling theory of entanglement entropy in confinements near quantum critical points
• Driving Driven Lattice Gases to Identify Their Universality Classes
• Scaling in driven dynamics starting in the vicinity of a quantum critical point
• Holographic topological defects and local gauge symmetry: clusters of strongly coupled equal-sign vortices
• Self-similarity breaking: Anomalous nonequilibrium finite-size scaling and finite-time scaling
• Theory of Critical Phenomena with Memory
• Theory of Critical Phenomena with Long-Range Temporal Interaction
• Finite-time scaling with two characteristic time scales: Driven critical dynamics with emergent symmetry
• Anomalous Dynamical Scaling at Topological Quantum Criticality