Large Deviations Beyond the Kibble-Zurek Mechanism

TL;DR

This paper extends the understanding of defect number fluctuations beyond the Kibble-Zurek mechanism by applying large deviations theory to quantum phase transitions, providing exact results and universal scaling laws.

Contribution

It introduces a large deviations framework to characterize the universality of defect fluctuations beyond the KZM, including exact rate functions for the quantum Ising model.

Findings

Exact form of the rate function in the quantum Ising model

Universality of defect number distribution near phase transitions

Scaling laws for large deviations in continuous phase transitions

Abstract

The Kibble-Zurek mechanism (KZM) predicts that the average number of topological defects generated upon crossing a continuous or quantum phase transition obeys a universal scaling law with the quench time. Fluctuations in the defect number near equilibrium are approximately of Gaussian form, in agreement with the central limit theorem. Using large deviations theory, we characterize the universality of fluctuations beyond the KZM and report the exact form of the rate function in the transverse-field quantum Ising model. In addition, we characterize the scaling of large deviations in an arbitrary continuous phase transition, building on recent evidence establishing the universality of the defect number distribution.