Universality and weak-ergodicity breaking in quantum quenches

Understanding equilibration and universality after sudden quantum quenches remains a central challenge in isolated many-body systems. Persistent oscillations and anomalous scaling reported in lattice models appear to challenge the standard picture based on integrability and quantum-to-classical correspondence. Focusing on the quantum $O(n)$ model in the large-$n$ limit, we show that these apparent anomalies originate from lattice effects and an underlying integrable structure. In particular, we map the post-quench dynamics onto an integrable Neumann system and we derive a new action-angle description valid in the thermodynamic limit. This framework explains both the convergence of long-time averages to the generalized Gibbs ensemble and the emergence of persistent oscillations associated with an isolated mode at the upper edge of the phonon spectrum. We further show that the expected thermal universality class is recovered in the appropriate scaling regime, while the oscillations disappear in the quantum field theory limit.