Nuclear relaxation in the spin-$1/2$ antiferromagnetic chain compound ${\mathrm{Sr}}_2{\mathrm{CuO}}_3:$ Comparison between theories and experiments

The NMR relaxation data on ${\mathrm{Sr}}_2{\mathrm{CuO}}_3$ [Phys. Rev. Lett. 76, 4612 (1996)] are reexamined and compared with the analytic theory of the dynamic susceptibility in the $S=1/2\mathrm{}$ antiferromagnetic Heisenberg chain including multiplicative logarithmic corrections [Phys. Rev. Lett. 78, 539 (1997)]. Comparisons of the spin-lattice and the Gaussian spin-echo decay rates (${1/T}_1$ and ${1/T}_{2G}$) and their ratio all show good quantitative agreement. Our results demonstrate the importance of the logarithmic corrections in the analysis of experimental data for quasi-one-dimensional systems and indicate that the dynamics of ${\mathrm{Sr}}_2{\mathrm{CuO}}_3$ is well described by an $S=1/2\mathrm{}$ one-dimensional Heisenberg model with a nearest-neighbor exchange.