  We study energy transport in the paradigmatic Hamiltonian mean-field (HMF)
model and other related long-range interacting models using molecular dynamics
simulations. We show that energy diffusion in the HMF model is subdiffusive in
nature, which confirms a recently obtained intriguing result that, despite
being globally interacting, this model is a thermal insulator in the thermo-
dynamic limit. Surprisingly, when additional nearest neighbor interactions are
introduced to the HMF model, an energy superdiffusion is observed. We show that
these results can be consistently explained by studying energy localization due
to thermally generated intrinsic localized excitation modes (discrete
breathers) in nonlinear discrete systems. Our analysis for the HMF model can
also be readily extended to more generic long-range interacting models where
the interaction strength decays algebraically with the (shortest) distance
between two lattice sites. This reconciles many of the apparently
counter-intuitive results presented recently [C. Olivares and C. Anteneodo,
Phys. Rev. E 94, 042117 (2016); D. Bagchi, Phys. Rev. E 95, 032102 (2017)]
concerning energy transport in two such long-range interacting models.
