NMR relaxation rates in a spin-12antiferromagnetic chain

We consider the low-temperature behavior of NMR relaxation rates $T_1$ and $T_{2G}$ in the spin-$1/2$ antiferromagnetic chain. We find that $T_1\propto \mathrm{const}$ and $T_{2G}\propto \sqrt{T},$ with logarithmic corrections. We determine both constants and logarithmic terms by matching perturbative renormalization-group with exact results, so that the final expressions for the relaxation rates do not contain any free parameters. Our theoretical results are in excellent agreement with NMR experiments in ${\mathrm{Sr}}_2{\mathrm{CuO}}_3.$