  We consider heat transfer in one-dimensional systems with long-range
interactions. It is known that typical short-range interacting systems shows
anomalous behavior in heat transport when total momentum is conserved, whereas
momentum-nonconserving systems do not exhibit anomaly. In this study, we focus
on the effect of long-range interaction. We propose an exactly solvable model
that reduces to the so-called momentum-exchange model in the short-range
interaction limit. We exactly calculate the asymptotic time-decay in the energy
current correlation function, which is related to the thermal conductivity via
the Green--Kubo formula. From the time-decay of the current correlation, we
show three qualitatively crucial results. First, the anomalous exponent in the
time-decay {\it continuously} changes as a function of the index of the
long-range interaction. Second, there is a regime where the current correlation
diverges as increasing the system size with fixed time, and hence the exponent
of the time-decay cannot be defined. Third, even momentum-nonconserving systems
can show the anomalous exponent indicating anomalous heat transport.
Higher-dimensions are also considered, and we found that long-range interaction
can induce anomalous exponent even in the three-dimensional systems.
