Quantum Critical Scaling and Temperature-Dependent Logarithmic Corrections in the Spin-Half Heisenberg Chain

Low temperature dynamics of the $S=\frac{1}{2}$ Heisenberg chain is studied via a simple ansatz generalizing the conformal mapping and analytic continuation procedures to correlation functions with multiplicative logarithmic factors. Closed form expressions for the dynamic susceptibility and the NMR relaxation rates $1/T_1$ and $1/T_{2G}$ are obtained, and are argued to improve the agreement with recent experiments. Scaling in $q/T$ and $\omega /T$ are violated due to these logarithmic terms. Numerical results show that the logarithmic corrections are very robust. While not yet in the asymptotic low temperature regime, they provide striking qualitative confirmation of the theoretical results.