Separation of the Kibble-Zurek Mechanism from Quantum Criticality

TL;DR

This paper investigates the relationship between the Kibble-Zurek mechanism and quantum criticality, revealing that their correspondence is not universal and identifying conditions for defect scaling.

Contribution

It demonstrates that Kibble-Zurek scaling can be suppressed or persist independently of criticality, clarifying the dynamical conditions for universal defect scaling.

Findings

Defect density can be suppressed faster than Kibble-Zurek prediction.

Kibble-Zurek scaling may persist even when crossing non-critical points.

The relation between defect generation and criticality is model-dependent.

Abstract

When a system is swept through a quantum critical point (QCP), the Kibble-Zurek mechanism predicts that the average number of topological defects follows a universal power-law scaling with the ramp time scale. This scaling behavior is determined by the equilibrium critical exponents of the underlying phase transition. We show that the correspondence between Kibble-Zurek scaling and quantum criticality does not hold generally. In particular, the defect density can exhibit a suppression faster than the Kibble-Zurek prediction even when the quench crosses a critical point, while conventional Kibble-Zurek scaling may persist for quenches through a non-critical point. Our results, based on models representative of a broad class of quasi-one-dimensional Fermi systems, identify the dynamical conditions under which universal defect scaling emerges and clarify the relation between defect generation and equilibrium criticality.