  We study the heat current autocorrelation function (HCAF) in one-dimensional,
momentum-conserving lattices. In particular, we explore if there is any
relation between the decaying characteristics of the HCAF and asymmetric
interparticle interactions. The Lennard-Jones model is intensively investigated
in view of its significance to applications. It is found that in wide ranges of
parameters, the HCAF decays faster than power-law manners, and in some cases it
decays even exponentially. Following the Green-Kubo formula, the fast decay of
HCAF implies the convergence of heat conductivity, which is also corroborated
by numerical simulations. In addition, with a comparison to the
Fermi-Pasta-Ulam-$\beta$ model of symmetric interaction, the HCAF of the
Fermi-Pasta-Ulam-$\alpha$-$\beta$ model of asymmetric interaction is also
investigated. Our study suggests that, in certain ranges of parameters, the
decaying behavior of the HCAF is correlated to the asymmetry degree of
interaction.
