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We study heat transfer in one-dimensional Fermi-Pasta-Ulam-Tsingou typesystems with long-range (LR) interactions. The strength of the LR interactionbetween two lattice sites decays as a power $\sigma$ of the inverse of theirdistance. We focus on the strong LR regime ($0\leq \sigma \leq1$) and show thatthe thermal transport behaviors are remarkably nuanced. Specifically, weobserve that the antipersistent (negative) energy current correlation in thisregime is intricately dependent on $\sigma$, displaying a nonmonotonicvariation. Notably, a significant qualitative change occurs at $\sigma_c=1/2$,where with respect to other $\sigma$ values, the correlation shows a minimumnegative value. The underlying mechanisms of this intriguing phenomenon isrelated to the two diverse space-time scaling properties of equilibrium heatcorrelations and the various scattering processes of phonons and discretebreathers.

Antipersistent energy current correlations in strong long-ranged Fermi-Pasta-Ulam-Tsingou type models