Transport anomaly in the low energy regime of spin chains

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.