# Universal power-law Kibble-Zurek scaling in fast quenches

Thomas Kibble’s research on phase transitions and topological defects is most significant. Actually, the Kibble-Zurek mechanism (KZM) is a paradigmatic theory to describe the dynamics across both classical continuous phase transitions and quantum phase transitions.

The Kibble-Zurek mechanism describes the non-equilibrium dynamics and the formation of topological defects in a system which is driven through a continuous phase transition at finite rate. It is named after Kibble, who pioneered the study of domain structure formation in the early universe, and Wojciech H. Zurek, who related the number of defects it creates to the critical exponents of the transition and to how quickly the critical point is traversed.

The development of new methods to induce or mimic adiabatic dynamics – where time flows very slowly and the solution of the Schrödinger’s equation at one given time goes continuously over to the solution at another time – is essential to the progress of quantum technologies. In many-body systems, the need to develop new methods to approach adiabatic dynamics is underlined for their potential application to quantum simulation and adiabatic quantum computation.

But there is a problem. Usually, the system of interest is assumed to be driven by a quenching of an external control parameter in a finite time across the critical value. KZM predicts that the average domain size exhibits a universal power-law scaling and that, at the boundary between domains, topological defects form. In other words, KZM constitutes a negative result for the purpose of suppressing defect formation, given that in an arbitrarily large system, defects will be formed no matter how slowly the phase transition is crossed.

Now, a team of researchers focuses ^{1} on the deviations from KZM experimentally observed in rapid quenches and establish their universality. While KZM scaling holds below a critical quench rate, for faster quenches the defect density and the freeze-out time become independent of the quench rate and exhibit a universal power-law scaling with the final value of the control parameter

Numerical simulations indicate the breakdown of the KZM scaling laws with the onset of a plateau in which the defect density is independent of the quench rate. This has been shown to happen in confined ion chains, holographic superconducting rings, or a one-dimensional quantum ferromagnet. As long as the quench time is shorter than the timescale in which the order parameter grows, the defect formation dynamics is insensitive to the quench rates and yields a constant defect density. Experimentally, deviations from KZM have been observed in ultracold Bose and Fermi gases driven through the normal-to-superfluid phase transition by a rapid quench.

The researchers show that the plateau defect density, associated freeze-out time, and the critical quench rate to scale with the amplitude of the quenching following universal power laws. They confirmed these predictions in a classical lattice model of relevance to ion chains, as well as a one-dimensional quantum Ising chain, thus establishing the universality of fast critical dynamics in the quantum domain.

These results broaden the application of equilibrium scaling theory to nonequilibrium phenomena in the limit of fast quenches, without restrictions to slow driving or adiabatic perturbation theory. The scaling laws predicted here are directly testable in any platform previously used to explore KZM in either the classical or quantum regimes.

*Author: César Tomé López is a science writer and the editor of Mapping Ignorance*

*Disclaimer: Parts of this article may have been copied verbatim or almost verbatim from the referenced research paper/s.*

## References

- Hua-Bi Zeng, Chuan-Yin Xia, and Adolfo del Campo (2023) Universal Breakdown of Kibble-Zurek Scaling in Fast Quenches across a Phase Transition
*Phys. Rev. Lett.*doi: 10.1103/PhysRevLett.130.060402 ↩