Quenches across a quantum critical point in a finite time frame exhibit non-adiabatic dynamics, prompting a reexamination of the Kibble-Zurek mechanism's applicability. The KZ framework, typically used to determine local observables like mean defect density, falls short in accounting for higher-point functions. Recent studies have demonstrated the need to transcend the KZ paradigm to accurately capture the behavior of quantum systems undergoing second-order phase transitions1. This has significant implications for the understanding of quantum criticality and its associated dynamics. The exploration of kink-kink correlations in nonlinear quenches is a crucial step towards a more comprehensive understanding of these complex phenomena. As quantum computing continues to advance, a deeper understanding of quantum criticality will be essential for the development of robust and secure quantum systems. Therefore, this research matters to practitioners and informed readers because it has the potential to inform the design of quantum computing architectures and cryptography protocols that can withstand the challenges of quantum criticality.