  The anomalous thermal conductivity in spin chains observed in experiments is
studied for the low temperature regime. In the effective dynamics with most
realistic perturbations, the so-called Umklapp terms is irrelevant to reduce
mean free path in the energy transport at even finite temperatures. This is
consistent with large conductivities found in recent experiments. The Drude
weight which is the prefactor in the divergent conductivity is calculated, and
the temperature dependence is discussed.
