Topological Defect Formation Beyond the Kibble-Zurek Mechanism in Crossover Transitions with Approximate Symmetries

TL;DR

This paper investigates how topological defect formation during phase transitions deviates from the Kibble-Zurek mechanism when symmetries are only approximate, revealing exponential corrections and proposing a generalized framework for these scenarios.

Contribution

It introduces a generalized model that accounts for explicit symmetry breaking effects, extending the understanding of defect formation beyond the traditional Kibble-Zurek mechanism.

Findings

Universal power-law scaling breaks down with exponential corrections.

Defect density depends on explicit symmetry breaking source.

Generalized framework accurately predicts defect formation across quench rates.

Abstract

The formation of topological defects during continuous second-order phase transitions is well described by the Kibble-Zurek mechanism (KZM). However, when the spontaneously broken symmetry is only approximate, such transitions become smooth crossovers, and the applicability of KZM in these scenarios remains an open question. In this work, we address this problem by analyzing both a weakly coupled Ginzburg-Landau model and a strongly coupled holographic setup, each featuring pseudo-spontaneous breaking of a global U(1) symmetry. In the slow quench regime, we observe a breakdown of the universal power-law scaling predicted by the Kibble-Zurek Mechanism. Specifically, the defect density acquires an exponential correction dependent on the quench rate, following a universal form dictated by the source of explicit symmetry breaking. Although these dynamics extend beyond the scope of the traditional KZM, we demonstrate that a generalized framework, that incorporates the effects of explicit symmetry breaking into the dynamical correlation length, remains valid and accurately captures the non-equilibrium defect formation across the entire range of quench rates.