  The persistence of effective light cones in long-range interacting quantum
systems remains a significant and intriguing conundrum. In this paper, we
theoretically reveal a mechanism in Heisenberg spin chains at low temperatures,
wherein subsystems resist entanglement despite the onset of entangling effects
in quench scenarios. This mechanism is attributed to destructive interference
among quasi-particles outside an effective light cone. Furthermore, we
establish a necessary condition for the occurrence of the destructive
interference phenomenon. We demonstrate that for 1-D power-law decay
interactions, specifically those following $|d_{ij}|^{-p}$, destructive
interference occurs when $p>2$. As shown through theoretical and numerical
analysis, this destructive interference results in an unexpected acceleration
of entanglement propagation when the interaction range is truncated. This
prediction is proposed to be observable experimentally in chains of trapped
ions as a direct manifestation of the destructive interference effect.
