Locality of Spontaneous Symmetry Breaking and Universal Spacing Distribution of Topological Defects Formed Across a Phase Transition

Abstract

The crossing of a continuous phase transition results in the formation of topological defects with a density predicted by the Kibble-Zurek mechanism (KZM). We characterize the spatial distribution of point-like topological defects in the resulting nonequilibrium state and model it using a Poisson point process in arbitrary spatial dimension with KZM density. Numerical simulations in a one-dimensional ${\varphi }^4$ theory unveil short-distance defect-defect corrections stemming from the kink excluded volume, while in two spatial dimensions, our model accurately describes the vortex spacing distribution in a strongly-coupled superconductor indicating the suppression of defect-defect spatial correlations.

Main text: 7 pages, 3 Figures. Appendixes: 5 pages, and 2 Figures

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• Structural phase transition and its critical dynamics from holography
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• Driving a Quantum Phase Transition at Arbitrary Rate: Exact solution of the Transverse-Field Ising model
• From black hole to one-dimensional chain: parity symmetry breaking and kink formation
• Universal Critical Holography and Domain Wall Formation
• Kibble-Zurek Mechanism and Beyond: Lessons from a Holographic Superfluid Disk
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• Spatial Form Factor for Point Patterns: Poisson Point Process, Coulomb Gas, and Vortex Statistics
• Anomalous Dynamical Scaling at Topological Quantum Criticality