We present a temperature and magnetic field dependence study of spin transport and magnetothermal corrections to the thermal conductivity in the spin S = 1/2 integrable easy-plane regime Heisenberg chain, extending an earlier analysis based on the Bethe ansatz method. We critically discuss the low temperature, weak magnetic field behavior, the effect of magnetothermal corrections in the vicinity of the critical field and their role in recent thermal conductivity experiments in 1D quantum magnets.
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