Prediction for spin Fano factor generated by biased quantum spin chains

We theoretically study noise in the spin current injected into a normal metal from a 1D Heisenberg spin-$1/2$ antiferromagnet. We consider the noise generated in two separate scenarios: first by inducing an over-population of one chiral mode relative to the other in the spin chain at uniform temperature, and second by elevating the temperature of the spin chain relative to the metal, i.e., by way of the spin Seebeck effect. We compute excess noise in the normal metal generated by the coupling to the spin chain and predict the spin Fano factor, defined as the noise in the spin current normalized by the average spin current, for both scenarios.