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

Large Deviations Beyond the Kibble-Zurek Mechanism