Abstract
Traversing a continuous phase transition at a finite rate leads to the breakdown of adiabatic dynamics and the formation of topological defects, as predicted by the celebrated Kibble-Zurek mechanism (KZM). We investigate universal signatures beyond the KZM, by characterizing the distribution of vortices generated in a thermal quench leading to the formation of a holographic superconductor. The full counting statistics of vortices is described by a binomial distribution, in which the mean value is dictated by the KZM and higher-order cumulants share the universal power-law scaling with the quench time. Extreme events associated with large fluctuations no longer exhibit a power-law behavior with the quench time and are characterized by a universal form of the Weibull distribution for different quench rates.
Highlights
Extreme events associated with large fluctuations no longer exhibit a power-law behavior with the quench time and are characterized by a universal form of the Weibull distribution for different quench rates
The full counting statistics of vortices is described by a binomial distribution, in which the mean value is dictated by the Kibble-Zurek mechanism (KZM) and higher-order cumulants share the universal power-law scaling with the quench time
The characterization of the full distribution of topological defects generated across a phase transition is expected to have wide applications, ranging from condensed matter to quantum simulation and computation, and cosmology
Summary
We simulate the superconducting transition from a normal metal to a holographic typeII superconductor in two spatial dimensions by implementing a thermal quench in a finite time τQ This results in the spontaneous formation of vortices that are pinned. According to the KZM, traversing the phase transition at finite rate leads to the formation of domains of characteristic length scale ξ =. According to the geodesic rule [3], when multiple domains merge at a point, there is a chance that the quantized circulation of the superconductor phase φ around that point is non-zero and a multiple 2π This configuration can lead to the formation of a vortex. Knowledge of the exact vortex number distribution allows us to characterize extreme events associated with large deviations from the mean value
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