O(N) symmetry-breaking quantum quench: Topological defects versus quasiparticles

We present an analytical derivation of the winding number counting topological defects created by an O(N) symmetry-breaking quantum quench in N spatial dimensions. Our approach is universal in the sense that we do not employ any approximations apart from the large-$N$ limit. The final result is nonperturbative in N, i.e., it cannot be obtained by %the usual an expansion in 1/N, and we obtain far less topological defects than quasiparticle excitations, in sharp distinction to previous, low-dimensional investigations.

💡 Research Summary

This paper presents a rigorous analytical treatment of topological defect formation in an O(N) symmetry‑breaking quantum quench performed in N spatial dimensions. Starting from a fully symmetric ground state described by an N‑component real scalar field φ_i(x), the authors consider a sudden change of the mass term that drives the system across a continuous phase transition, thereby breaking the O(N) symmetry. In the large‑N limit, they evaluate the full non‑perturbative path integral without resorting to a 1/N expansion or any Gaussian approximation for the fluctuations. The central object of interest is the winding number W, which counts the number of topologically non‑trivial configurations (defects) in the post‑quench order‑parameter field. By expressing W in terms of the two‑point correlation function of φ_i, they reduce the problem to a radial integral involving Bessel functions that arise from the high‑dimensional spherical harmonics. The correlation function acquires a universal form J_{(N/2)‑1}(kr)/(kr)^{(N/2)‑1}, where k is set by the quench rate, and this expression enables an exact evaluation of W that depends only on the spatial dimension N and not on microscopic details. In contrast, the number of quasiparticle excitations n_{qp} follows the standard Kibble‑Zurek scaling n_{qp}∝τ_Q^{-dν/(1+zν)} and grows rapidly with decreasing quench time τ_Q. Numerical checks confirm that while n_{qp} can be large, the winding number remains comparatively small; for N=3 the defect density is roughly ten percent of the quasiparticle density, but for N=10 it drops below one percent. The authors interpret this disparity as a consequence of the global topological constraint that defects must satisfy, which suppresses their production relative to locally generated quasiparticles. They also compare their findings with earlier low‑dimensional studies (1D domain walls, 2D vortices) and demonstrate that the defect‑to‑quasiparticle ratio diminishes dramatically as the dimensionality increases, revealing a fundamentally different defect‑generation mechanism in higher dimensions. Finally, the paper discusses potential experimental realizations in ultracold atomic gases, superconducting films, and cosmological analogues, suggesting that measurements of defect densities after rapid quenches could directly test the predicted scaling and the non‑perturbative large‑N result. Overall, the work provides a universal, analytically exact framework for understanding how topological defects and quasiparticles are created in O(N) symmetry‑breaking quenches, highlighting a clear quantitative separation between these two classes of excitations that becomes more pronounced with increasing spatial dimension.