  We study heat transfer in one-dimensional Fermi-Pasta-Ulam-Tsingou type
systems with long-range (LR) interactions. The strength of the LR interaction
between two lattice sites decays as a power $\sigma$ of the inverse of their
distance. We focus on the strong LR regime ($0\leq \sigma \leq1$) and show that
the thermal transport behaviors are remarkably nuanced. Specifically, we
observe that the antipersistent (negative) energy current correlation in this
regime is intricately dependent on $\sigma$, displaying a nonmonotonic
variation. Notably, a significant qualitative change occurs at $\sigma_c=0.5$,
where with respect to other $\sigma$ values, the correlation shows a minimum
negative value. Furthermore, our findings also demonstrate that within the
long-time range considered, these antipersistent correlations will eventually
vanish for certain $\sigma >0.5$. The underlying mechanisms behind these
intriguing phenomena are related to the crossover of two diverse space-time
scaling properties of equilibrium heat correlations and the various scattering
processes of phonons and discrete breathers.
