NMR relaxation rates for the spin-1/2 Heisenberg chain

The spin-lattice relaxation rate 1/${\mathit{T}}_1$ and the spin-echo decay rate 1/${\mathit{T}}_{2\mathit{G}}$ for the spin-1/2 antiferromagnetic Heisenberg chain are calculated using quantum Monte Carlo and maximum-entropy analytic continuation. The results are compared with recent analytical calculations by Sachdev. If the nuclear hyperfine form factor ${\mathit{A}}_{\mathit{q}}$ is strongly peaked around q=π, the predicted low-temperature behavior [1/${\mathit{T}}_1$∼${\ln }^{1/2}$(1/T), 1/${\mathit{T}}_{2\mathit{G}}$∼${\ln }^{1/2}$(1/T)/√T] extends up to temperatures as high as T/J≊0.5. If ${\mathit{A}}_{\mathit{q}}$ has significant weight for q≊0 there are large contributions from diffusive long-wavelength processes not taken into account in the theory, and very low temperatures are needed in order to observe the asymptotic T→0 forms.