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We investigate heat transport in various quantum spin chains, using theprojector operator technique. We find that anomalous heat transport is linkednot to the integrability of the Hamiltonian, but to whether it can be mapped toa model of non-interacting fermions. Our results also suggest how seeminglyanomalous transport may occur at low temperatures in a much wider class ofmodels.

Heat transport in quantum spin chains: the relevance of integrability