Universality and weak-ergodicity breaking in quantum quenches

Sudden quenches in quantum many-body systems often lead to dynamical evolutions that unveil surprising physical behaviors. In this work, we argue that the emergence of weak ergodicity breaking following quantum quenches in certain local many-body systems is a direct consequence of lattice discretization. To support this claim, we investigate the out-of-equilibrium dynamics of quantum $O(n)$ models on a lattice. In doing so, we also revisit two puzzling results in the literature on quantum $O(n)$ models, concerning universal scaling and equilibration, and demonstrate how these apparent contradictions can be resolved by properly accounting for lattice effects.