System size scaling of topological defect creation in a second-order dynamical quantum phase transition

TL;DR

This paper studies how the number of topological defects created during a second-order quantum phase transition scales with system size, revealing surface-area and dimension-dependent behaviors.

Contribution

It introduces a mean-field approach to analyze defect scaling in large N systems, highlighting the impact of symmetries and correlations on defect variance.

Findings

Defect variance scales with surface area in short-range correlated systems.

In systems with broken isotropy and long-range correlations, scaling depends on the dimension being even or odd.

For even dimensions, defect variance scales with surface area squared, with oscillations; for odd, it vanishes.

Abstract

We investigate the system size scaling of the net defect number created by a rapid quench in a second-order quantum phase transition from an O(N) symmetric state to a phase of broken symmetry. Using a controlled mean-field expansion for large N, we find that the net defect number variance in convex volumina scales like the surface area of the sample for short-range correlations. This behaviour follows generally from spatial and internal symmetries. Conversely, if spatial isotropy is broken, e.g., by a lattice, and in addition long-range periodic correlations develop in the broken-symmetry phase, we get the rather counterintuitive result that the scaling strongly depends on the dimension being even or odd: For even dimensions, the net defect number variance scales like the surface area squared, with a prefactor oscillating with the system size, while for odd dimensions, it essentially vanishes.