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The anomalous thermal conductivity in spin chains observed in experiments isstudied for the low temperature regime. In the effective dynamics with mostrealistic perturbations, the so-called Umklapp terms is irrelevant to reducemean free path in the energy transport at even finite temperatures. This isconsistent with large conductivities found in recent experiments. The Drudeweight which is the prefactor in the divergent conductivity is calculated, andthe temperature dependence is discussed.Comment: 4 pages, no figure. PRB, in pres

Transport anomaly in the low-energy regime of spin chains