Tighter thermalization bounds for perturbed quantum many-body scars

Quantum many-body scars (QMBS) are exceptional eigenstates that defy thermalization, enabling long-lived coherent dynamics in strongly interacting systems. However, their stability under perturbations remains inadequately understood. In this work, we derive improved lower bounds on the thermalization time of QMBS under local perturbations with strength $\lambda$. Using both numerical simulations and analytical reasoning, we show that exact QMBS exhibit slow thermalization, with a timescale scaling as $\tau \sim \mathcal{O}(\lambda^{-1/d})$ owing to the stabilizing restricted spectrum-generating algebra (RSGA), which is a significant improvement over previous bounds (e.g., $\tau \sim \mathcal{O}(\lambda^{-1/(d+1)})$). Counterintuitively, approximate QMBS can thermalize even more slowly under generic perturbations, exhibiting $\tau \sim \mathcal{O}(\lambda^{-2})$ scaling due to second-order perturbative effects in the absence of such protective structure. These distinct thermalization behaviors clarify how exact and approximate scars maintain coherence. Our work advances previous findings by establishing a tighter bound on the thermalization time, clarifying when scarred dynamics remain long-lived under weak but generic perturbations.