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We identify persistent oscillations in a nonintegrable quantum Ising chain left behind by a rapid transition into a ferromagnetic phase. In the integrable chain with nearest-neighbor (NN) interactions, the nature, origin, and decay of post-transition oscillations are tied to the Kibble-Zurek mechanism (KZM). However, when coupling to the next nearest neighbor (NNN) is added, the resulting nonintegrable Ising chain (still in the quantum Ising chain universality class) supports persistent post-transition oscillation: KZM-like oscillations turn into persistent oscillations of transverse magnetization. Their longevity in our simulations is likely limited only by the numerical accuracy. Their period differs from the decaying KZM oscillation but their amplitude depends on quench rate. Moreover, they can be excited by driving in resonance with the excitations' energy gap. Thus, while one might have expected that the integrability-breaking NNN coupling would facilitate relaxation, the oscillations we identify are persistent. At low to medium transverse fields, they are associated with Cooper pairs of Bogoliubov quasiparticles -- kinks. This oscillation of the pair condensate is a manifestation of quantum coherence.
Bayocboc et al. (Mon,) studied this question.