Kibble-Zurek Mechanism and Beyond: Lessons from a Holographic Superfluid Disk

TL;DR

This study uses holographic duality to analyze superfluid phase transition dynamics, revealing universal scaling laws for vortex formation that extend beyond traditional Kibble-Zurek predictions, especially at fast quenches.

Contribution

It demonstrates universal vortex scaling laws in a holographic superfluid, including deviations from KZM at fast quenches, and characterizes vortex statistics with a Poisson binomial distribution.

Findings

Vortex density follows KZM scaling for slow quenches.

At fast quenches, vortex density scales with final temperature, beyond KZM.

Vortex number distribution approximates a normal distribution, with non-normal features in cumulants.

Abstract

The superfluid phase transition dynamics and associated spontaneous vortex formation with the crossing of the critical temperature in a disk geometry is studied in the framework of the $AdS/CFT$ correspondence by solving the Einstein-Abelian-Higgs model in an $AdS_4$ black hole. For a slow quench, the vortex density admits a universal scaling law with the cooling rate as predicted by the Kibble-Zurek mechanism (KZM), while for fast quenches, the density shows a universal scaling behavior as a function of the final temperature, that lies beyond the KZM prediction. The vortex number distribution in both the power-law and saturation regimes can be approximated by a normal distribution. However, the study of the universal scaling of the cumulants reveals non-normal features and indicates that vortex statistics in the newborn superfluid is best described by the Poisson binomial distribution, previously predicted in the KZM regime [Phys. Rev. Lett. 124, 240602 (2020)]. This is confirmed by studying the cumulant scalings as a function of the quench time and the quench depth. Our work supports the existence of a universal defect number distribution that accommodates the KZM scaling, its breakdown at fast quenches, and the additional universal scaling laws as a function of the final value of the control parameter.