Diverging magnetothermal response in the one-dimensional Heisenberg chain

A current of magnetic moments will flow in the spin-1/2 Heisenberg chain in the presence of an external magnetic field $B$ and a temperature gradient $\Delta T$ along the chain. We show that this magnetothermal effect is strictly {\em infinite} for the integrable Heisenberg-model in one dimension. We set-up the response formalism and derive several new generalized Einstein relations for this magnetothermal effect which vanishes in the absence of an external magnetic field. We estimate the size of the magnetothermal response by exact diagonalization and Quantum Monte Carlo and make contact with recent transport measurements for the one-dimensional Heisenberg compound $\rm Sr_2CuO_3$.