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

TL;DR

This paper analytically derives the number of topological defects formed during an O(N) symmetry-breaking quantum quench in N dimensions, revealing a universal, nonperturbative result that shows fewer defects than quasiparticles, contrasting with earlier low-dimensional studies.

Contribution

It provides a universal, nonperturbative analytical derivation of defect formation in high-dimensional quantum quenches without approximations besides the large-N limit.

Findings

Fewer topological defects than quasiparticles are created.

The derivation is nonperturbative in N.

Results differ from low-dimensional cases.

Abstract

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.