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

The spin-lattice relaxation rate 1/T₁ and the spin-echo decay rate 1/T_2G 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 A_q is strongly peaked around q=π, the predicted low-temperature behavior [1/T₁∼ln^1/2(1/T), 1/T_2G∼ln^1/2(1/T)/√T] extends up to temperatures as high as T/J≊0.5. If A_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.